test.json

[
    {
        "instruction": "An object of mass 298 g stands on a weighing machine in a lift, which is moving downwards with a uniform speed of 737 cm/s.",
        "input": "Scale Reading = m * 10 - v",
        "output": "2243\nTo calculate the scale reading, we use the formula Scale Reading = mass * 10 - velocity, where the mass is 298 g and the velocity is 737 cm/s."
    },
    {
        "instruction": "A steady current of 10 A flows through a conductor, then calculate the time taken for 67203895955888402133 electrons to pass through any cross section of the conductor?",
        "input": "t = (n * e) / I",
        "output": "1.1 s\n\nThe time taken for the electrons to pass through any cross section of the conductor can be calculated using the formula: t = (n * e) / I, where n is the number of electrons, e is the charge of an electron, and I is the current."
    },
    {
        "instruction": "An Electric dipole with dipole moment 188 x 10^(-9) C-m is aligned at 148 degrees with the direction of a uniform electric field of magnitude 88 x 10^4 N C-1. Calculate the magnitude of torque acting on the dipole?\n",
        "input": "Torque = dipole moment * electric field * sin(theta)\n",
        "output": "The torque acting on an electric dipole in a uniform electric field can be calculated using the formula:\nSubstituting the given values:\nTorque = 188 x 10^(-9) C-m * 88 x 10^4 N C-1 * sin(148)\nTorque = 8.8e+03 newton-m\n"
    },
    {
        "instruction": "The frequency of sound is 579 Hz.How many times does it vibrate in 395 seconds?\n",
        "input": "Number of vibrations = frequency*time",
        "output": "228705 \nTo calculate the number of vibrations (cycles) of a sound wave in a given time, we can use the formula: Number of vibrations = frequency \u00d7 time. In this case, the frequency of the sound wave is 579 Hz and the time is 395 seconds. Substituting these values into the formula, we can calculate the number of vibrations: Number of vibrations = 579 Hz \u00d7 395 s"
    },
    {
        "instruction": "Suppose that the electric field part of an electromagnetic wave in vacuum is E = 1846cos[912y + 328947t]. What is the amplitude of the magnetic field part of the wave?",
        "input": "E0 = 1846 N/C",
        "output": "6.15e-06 tesla\n\nThe magnetic field amplitude can be calculated by dividing the electric field amplitude by the speed of light."
    },
    {
        "instruction": "A rectangular wire loop of sides 27 cm and 13 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 15.5 T directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is 37 cm/s in a direction normal to the two different sides of the loop? For how long does the induced voltage last in each case?\n",
        "input": "EMF = B * l * v",
        "output": "1.55e+00 volt for 7.30e-01 s if the velocity is perpendicular to the 27 cm side, 7.46e-01 volt for 3.51e-01 s if the velocity is perpendicular to the 13 cm side\n\n\nThe electromotive force (EMF) can be calculated using the formula EMF = B * l * v, where B is the magnetic field magnitude, l is the side length of the rectangular wire loop, and v is the velocity of the loop after conversion from cm/s to m/s."
    },
    {
        "instruction": "An electric appliance of 49388 W power rating is operated in a domestic electric circuit of 228 V that has a current rating of 88.3 A. Will the appliance be safe for a longer time?",
        "input": "P/V - I",
        "output": "It will be safer if P/V - I is less than or equal to 0.01. Now P/V - I = 49388/228 - 88.3 = 128.314. So, it will not be safe for a longer time."
    },
    {
        "instruction": "A refrigerator is to maintain eatables kept inside at -6 degree C, if room temperature is 84 degree C. Calculate the coefficient of performance.\n",
        "input": "Coefficient of performance = T2/T1-T2",
        "output": "3.0\nThis formula is only applicable if the refrigerator is based on the Carnot Cycle."
    },
    {
        "instruction": "A rope of negligible mass is wound round a hollow sphere of mass 94 kg and radius 12 cm. What is the angular acceleration of the hollow sphere if the rope is pulled with a force of 49 N? Assume that there is no slipping.",
        "input": "Acceleration = Force / (k * mass * radius)",
        "output": "Acceleration = 49 N / (0.6666666666666666 * 94 kg * 12 cm)\n\nTo calculate the angular acceleration of the hollow sphere, we use the following formula:\n\nAcceleration = Force / (k * mass * radius)\n\nSubstituting the values:\n\nForce = 49 N\nk = 0.6666666666666666\nMass = 94 kg\nRadius = 12 cm\n\nWe find that the angular acceleration of the hollow sphere is approximately 6.5 rad/s\u00b2."
    },
    {
        "instruction": "You are riding an automobile of mass 13100 kg. The suspension sags 47 cm when the entire automobile is placed on it. Also, the amplitude of oscillation decreases by 44 percent during one complete oscillation. Estimate the value of the damping constant b for the spring and shock absorber system of one wheel",
        "input": "",
        "output": "To estimate the value of the damping constant b, we first calculate the spring constant k using the formula (m * g) / (0.04 * x), where m is the mass of the automobile (13100 kg), g is the acceleration due to gravity (10 m/s^2), and x is the sag of the suspension (47 cm). Then, we use the formula (2 * m * ln(2) * log(10)) / (t), where m is the mass of the automobile (13100 kg) and t is the period of oscillation., this is the final answer: 6.67e+03 kgs-1"
    },
    {
        "instruction": "A sound wave travels at a speed of 338175.5 m/s, if it's wavelength is 13 m, will the sound wave be audible ? \n",
        "input": "frequency = wave speed / wavelength",
        "output": "not audible\nWhether a sound wave is audible or not depends on its frequency, not its wavelength. Audible sound waves have frequencies within the range of human hearing, which is typically between 20 Hz and 20,000 Hz. To determine if a sound wave is audible, we need to calculate its frequency using the wave speed and wavelength. The formula to calculate the frequency of a sound wave is: f = v / \u03bb, where f is the frequency, v is the wave speed, and \u03bb is the wavelength. Substituting the given values into the formula, we can calculate the frequency of the sound wave: f = 338175.5 m/s / 13 m. Now, we can compare the calculated frequency to the audible frequency range (20 Hz to 20,000 Hz) to determine if the sound wave is audible or not."
    },
    {
        "instruction": "Estimate the mean free path of a gas molecule in a cylinder containing gas at 39 atm and temperature 81 degree C. Take the radius of a gas molecule to be roughly 70 A.",
        "input": "mean_free_path = 1 / (sqrt(2) * pi * nu * (4 * r * r))",
        "output": "0.0 m\nHere, nu = (n * p) / (R * t1) = (6.022999999999999e+23 * 39 * 10^5) / (8.31 * 81 + 273) = 7.984968080115849e+26\nmean_free_path = 1 / (sqrt(2) * pi * 7.984968080115849e+26 * (4 * 70 * 10^-10 * 70 * 10^-10)) = 0.0"
    },
    {
        "instruction": "A spring with K = 979 Nm-1 is mounted on a table. A mass of 38 kg is attached to it. The mass is then pulled sideways by a distance of 49 cm and released. Assuming the spring is in the unstretched position at x = 0, with the direction from left to right as the positive x-axis, give x as a function of t when the mass is at mean position.",
        "input": "Formula: x = displacement * sin(wt)",
        "output": "Using this formula: Formula: x = displacement * sin(wt), this is the final answer derived: x = 49 sin(5t)"
    },
    {
        "instruction": "For the travelling harmonic wave y(x, t) = 44 cos 2\u03c0 (7t \u2013 0.025x + 0.35) where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of 13 m?\n",
        "input": "Phase difference = (2pi/wavelength)* Path difference",
        "output": "65.0 \u03c0 rad\nTo calculate the phase difference between two points in a traveling harmonic wave, we need to compare the phase angles of the wave at those points.In the given wave equation, the phase angle is represented by the term inside the cosine function, i.e., 2\u03c0(wt - kx + 0.35), where w represents the angular frequency and k represents the wave number.Let's assume the two points are at x1 and x2, separated by a distance \u0394x = x2 - x1. The phase difference between the oscillatory motion of these two points can be calculated using the equation: Phase difference = 2\u03c0(k\u0394x)"
    },
    {
        "instruction": "A particle starts from origin at t = 0 s with a velocity of (8) i + (2) j ms-1 and moves in x-y plane with a constant acceleration of (9) i + (5) j ms-2, then what is the time taken to reach the final velocity of 737 i + 407 j ms-1",
        "input": "v = u + a * t",
        "output": "t = 81 s"
    },
    {
        "instruction": "An oxygen cylinder of volume 32 litre has an initial gauge pressure of 16 atmosphere and a temperature of 36 degree C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 7 atmosphere and its temperature drops to 54 degree C. Estimate the number of moles of oxygen taken out of the cylinder.",
        "input": "n = (p1 * V) / (R * T1) - (p2 * V) / (R * T2)",
        "output": "11.7 mol  (p1 * V) / (R * T1) - (p2 * V) / (R * T2)"
    },
    {
        "instruction": "In a chamber, a uniform magnetic field of 0.003 T is maintained. An electron is shot into the field with a speed of 30000000 m/s, making an angle of 25 degrees with the field. Determine the frequency of the revolution of the electron.",
        "input": "Frequency of revolution = (b * e) / (2 * pi * m)",
        "output": "To calculate the frequency of revolution, we use the following formula:\n\nFrequency of revolution = (b * e) / (2 * pi * m)\n\nSubstituting the given values:\n- b = 0.003 T\n- e = 1.6000000000000002e-19 C\n- m = 9.1e-31 kg\n\nAfter evaluating the formula, we find that the frequency of revolution is approximately 8.39e+07 sec^-1."
    },
    {
        "instruction": "Two moving coil meters M1 and M2 have the following particulars R1 = 6 ohms, N1 = 2, A1 = 0.00030000000000000003 m2 , B1 = 6 T, K1 = 7 and  R2 = 5 ohms, N2 = 9 , A1 = 0.0002 m2 , B1 = 10 T, K2 = 6. Determine the ratio of voltage sensitivities of M1 and M2.\n",
        "input": "Ratio of current sensitivity of M1 to M2 is given by, n1 x b1 x a1 x k2 : n2 x b2 x a2 x k1",
        "output": "Ratio of voltage sensitivity of M1 to M2 is is given by, n1 x b1 x a1 x k2 x r2 : n2 x b2 x a2 x k1 x r1 = 2 x 6 x 0.00030000000000000003 x 6 x 5 : 9 x 10 x 0.0002 x 7 x 6 = 0.2\n"
    },
    {
        "instruction": "What is the focal length of a concave lens of focal length 254 cm in contact with a convex lens of focal length 63 cm? Is the system a converging or a diverging lens? Ignore thickness of the lenses.",
        "input": "Formula: For two lenses in contact, the combined focal length (P) is given by P = (f1 * f2) / (f1 + f2), where f1 and f2 are the focal lengths of the lenses.",
        "output": "This is the answer {answer}, formula used is : {formula}"
    },
    {
        "instruction": "Torque of 952 Nm is transmitted to an engine at a power of 109 W. What is the angular speed of the rotor?",
        "input": "Angular Speed = Power / Torque",
        "output": "Angular Speed = 109 W / 952 Nm\n\nTo calculate the angular speed of the rotor, we use the following formula:\n\nAngular Speed = Power / Torque\n\nSubstituting the values:\n\nPower = 109 W\nTorque = 952 Nm\n\nWe find that the angular speed of the rotor is 0.1 rad/s."
    },
    {
        "instruction": "A wheel starting with an initial angular velocity of 4 rad/s accelerates with a constant angular acceleration of 73 rad/s\u00b2. If it reaches an angular position of 33 rad, then what is its final velocity?",
        "input": "final_angular_velocity = sqrt(initial_angular_velocity^2 + (2 * angular_acceleration * angular_position))",
        "output": "To calculate the final angular velocity, we use the following formula:\n\nfinal_angular_velocity = sqrt(initial_angular_velocity^2 + (2 * angular_acceleration * angular_position))\n\nSubstituting the given values into the formula, we find that the final angular velocity is approximately 69.5 rad/s."
    },
    {
        "instruction": "A wire of material-1 of length 165 m stretches by the same amount as a wire of material-2 of length 25 m under a given load. What is the ratio of the Young\u2019s modulus of material-1 to that of material-2, assuming the ratio of their cross-sectional areas is 1/8?",
        "input": "ratio = (l1 * A2) / (l2 * A1)",
        "output": "The ratio of the Young's modulus of material-1 to that of material-2 is approximately 52.80. To calculate the ratio, we use the formula:\n\nratio = (l1 * A2) / (l2 * A1)"
    },
    {
        "instruction": "Two sitar strings A and B playing the note \u2018Ga\u2019 are slightly out of tune and produce beats of frequency 22 Hz. The tension in the string A is slightly increased and the beat frequency is found to be 3 Hz. If the original frequency of A is 531 Hz, what is the frequency of B?\n",
        "input": "Beat frequency = |f1+-f2|",
        "output": "553 hertz\nFrequency decreases with a decrease in the tension of a string.\nThis is because frequency is directly proportional to the square root of tension."
    },
    {
        "instruction": "Find the ratio of time taken by the sound wave to travel a distance of 1 m in material-1 and material-2 (speed of sound in material-1 is 248 m/s, in material-2 is 9018 m/s) ?\n",
        "input": "Speed = Distance/Time",
        "output": "36.4\nTo find the ratio of the time taken by the sound wave to travel a distance of 1 m in material-1 and material-2, we can use the equation: Ratio of time = time in material-1 / time in material-2. The time taken by the sound wave to travel a distance in material-1 can be calculated using the equation: time in material-1 = distance / speed in material-1. Similarly, the time taken by the sound wave to travel the same distance in material-2 can be calculated using: time in material-2 = distance / speed in material-2. Substituting the given values into the equations, we have: time in material-1 = 1 m / 248 m/, time in material-2 = 1 m / 9018 m/s. Therefore, the ratio of the time taken by the sound wave to travel a distance of 1 m in material-1 and material-2 is: Ratio of time = (1 m / 248 m/s) / (1 m / 9018 m/s)= 36.36290322580645"
    },
    {
        "instruction": "A bat emits ultrasonic sound of frequency 1759036 Hz in air. If this sound meets a water surface, what is the wavelength of the reflected sound? (Speed of sound in air = 340 ms-1 and in water = 1486 ms-1)\n",
        "input": "wavelength of refracted sound = speed of sound in air/frequency of the ultrasonic sound",
        "output": "1.93e-04 m\nGiven that the speed of sound in air is 340 m/s and the speed of sound in water is 1486 m/s, we can substitute these values into the formula to calculate the wavelength. For the sound emitted in air: \u03bb_air = (340 m/s) / 1759036 Hz, For the sound reflected in water: \u03bb_water = (1486 m/s) / 1759036 Hz"
    },
    {
        "instruction": "A series LCR circuit is connected to a variable frequency 230 V source with L = 80 H, C = 12 muF, R = 149 ohm. Determine the source frequency which drives the circuit in resonance?",
        "input": "Source Frequency = 1 / sqrt(L * C)",
        "output": "Source Frequency = 32.3 rad/s"
    },
    {
        "instruction": "A body is dropped from a tower with an initial velocity of 194 m/s and reaches the ground after 106 s. With what velocity does it reach the ground?",
        "input": "velocity = initial_velocity + (acceleration * time)",
        "output": "The body reaches the ground with a velocity of 1232.8 m/s."
    },
    {
        "instruction": "A monkey of mass 32 kg climbs on a rope which can stand a maximum tension of 413 N. In which of the following cases will the rope break: the monkey\n(a) climbs up with an acceleration of 1 ms-2\n(b) climbs down with an acceleration of 3 ms-2\n(c) climbs up (or) down with a uniform speed of 9 ms-1\n",
        "input": "Tension = m * (10 + 1)\nTension = m * (10 - 3)\nTension = m * 10",
        "output": "(a) not break, (b) not break, (c) not break"
    },
    {
        "instruction": "A bat is flitting about in a cave, navigating via ultrasonic beeps. Assume that the sound emission frequency of the bat is 33860 Hz. During one fast swoop directly toward a flat wall surface, the bat is moving at 0.1816 times the speed of sound in air. What frequency does the bat hear reflected off the wall?\n",
        "input": "apparent frequency = [{(speed of air + speed of bat)}/speed of air]*apparent frequency of sound striking the wall",
        "output": "4.89e+04 hertz\nThe concept of Doppler's effect has been applied to calculate apparent frequencies."
    },
    {
        "instruction": "For a transistor as a switch in saturation state, the audio signal voltage across the collected resistance of 3610 ohm is 16 V. Suppose the current amplification factor of the transistor is 170, find the base current if the base resistance is 1470 ohm?\n",
        "input": "output voltage/input voltage = current amplification factor*output resistance/input resistance",
        "output": "voltage without amplification is 16/170 = 0.09, to get voltage per unit resistance, we need to divide it by 3610, the resultant voltage per unit resistance is current and it's value is 2.61e-05 ampere\n"
    },
    {
        "instruction": "A spring balance has a scale that reads from 0 to 168 kg. The length of the scale is 116 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 365 ms. What is the weight of the body?",
        "input": "Formula: w = (t^2 * k) / (4 * \u03c0^2), where w is the weight of the body, t is the period of oscillation (365 ms), and k is the spring constant given by (m * g) / (l * 0.01), where m is the reading on the scale (168 kg), g is the acceleration due to gravity (9.8 m/s^2), and l is the length of the scale (116 cm).",
        "output": "Using this formula: Formula: w = (t^2 * k) / (4 * \u03c0^2), where w is the weight of the body, t is the period of oscillation (365 ms), and k is the spring constant given by (m * g) / (l * 0.01), where m is the reading on the scale (168 kg), g is the acceleration due to gravity (9.8 m/s^2), and l is the length of the scale (116 cm)., this is the final answer derived: The spring constant k can be found out using the maximum mass and length of the scale as k = (m * g) / (l * 0.01), which is (168 * 9.8) / (1.16) = 1419.31.\nWe know that the time period of simple harmonic motion is given by t = 2\u03c0\u221a(m / k). From this equation, we can rearrange it to solve for m: m = (t^2 * k) / (4\u03c0^2).\nMultiplying the resulting mass with g, we get the weight, which is equal to (365^2 * 1419.31) / (4\u03c0^2) = 4.69e+01 newton."
    },
    {
        "instruction": "A large steel wheel is to be fitted onto a shaft of the same material. At 180 degree C, the outer diameter of the shaft is 154 cm and the diameter of the central hole in the wheel is 153.99 cm. The shaft is cooled using 'dry ice'. At what temperature of the shaft does the wheel slip on the shaft? Assume the coefficient of linear expansion of the steel to be constant over the required temperature range \u03b1steel = 1.20 x 10-5K-1.",
        "input": "Required temperature = t1 + ((d2 - d1) / (\u03b1 * d1))",
        "output": "To calculate the required temperature, we use the following formula:\n\nRequired temperature = t1 + ((d2 - d1) / (\u03b1 * d1))\n\nSubstituting the given values into the formula, we find that the temperature is approximately 176.8 degree C."
    },
    {
        "instruction": "The edge of a cube is 121 cm long. One face of the cube is firmly fixed to a vertical wall. A mass of 186 kg is then attached to the opposite face of the cube. The shear modulus of the material of the cube is 144 GPa. What is the vertical deflection of this face?",
        "input": "deflection = (mass * 9.8) / (Y * 10^9 * (edge_length * 10^-2))",
        "output": "To calculate the vertical deflection, we use the formula:\n\ndeflection = (mass * 9.8) / (Y * 10^9 * (edge_length * 10^-2))\n   = (186 kg * 9.8) / (144 * 10^9 GPa * (121 cm * 10^-2 m/cm))\n   = 10.5 nm."
    },
    {
        "instruction": "Let us assume that our galaxy consists of 82 * 10^9 stars each of one solar mass. How long will a star at a distance of 58300 ly from the galactic centre take to complete one revolution? Take the diameter of the Milky Way to be 10^5 ly.",
        "input": "No. of Stars = 82 * 10^9, Distance = 58300 ly",
        "output": "2.562e-05 s"
    },
    {
        "instruction": "Two long and parallel straight wires A and B carrying currents of 9 A and 24 A in the same direction are separated by a distance 43 cm. Estimate the force and its nature on the 30 cm section of wire A. (mu = 4 x pi x 10^(-7) TmA^-1)",
        "input": "Force = (mu * i1 * i2 * l) / (2 * pi * r)",
        "output": "To calculate the force and its nature, we use the following formula:\n\nForce = (mu * i1 * i2 * l) / (2 * pi * r)\n\nSubstituting the given values:\n- mu = 4 * pi * 10^(-7) TmA^-1\n- i1 = 9 A\n- i2 = 24 A\n- r = 43 cm\n- l = 30 cm\n\nAfter evaluating the formula, we find that the force on the 30 cm section of wire is approximately 3.01e-05 newtons and attractive."
    },
    {
        "instruction": "A sonar device on a submarine sends out a signal and receives an echo 302 s later. Find the distance of the object from the submarine if speed of sound in that material is 606 m/s ?\n",
        "input": "Distance = Speed * Time",
        "output": "91506.0 m\nTo find the distance of the object from the submarine, we can use the equation: Distance = Speed * Time. In this case, the speed of sound in the material is 606 m/s and the time it takes for the echo to return is 302 seconds. Substituting these values into the equation, we can calculate the distance of the object from the submarine: Distance = 606 m/s * 302 s. Calculating this expression will give us the distance of the object from the submarine."
    },
    {
        "instruction": "A uniformly charged conducting sphere of 1018 cm diameter has a surface charge density of 1726 micro-C/m\u00b2, then find the charge on the sphere?\n",
        "input": "Charge = Surface charge density * Surface area",
        "output": "To determine the charge on the sphere, we use the formula:\nCharge = Surface charge density * Surface area\nGiven surface charge density = 1726 micro-C/m\u00b2, diameter = 1018 cm,\nCharge = 5.62e-01 C\n"
    },
    {
        "instruction": "A rope of negligible mass is wound round a solid sphere of mass 2 kg and radius 69 cm. What is the angular acceleration of the solid sphere if the rope is pulled with a force of 16 N? Assume that there is no slipping.",
        "input": "Acceleration = Force / (k * mass * radius)",
        "output": "Acceleration = 16 N / (0.4 * 2 kg * 69 cm)\n\nTo calculate the angular acceleration of the solid sphere, we use the following formula:\n\nAcceleration = Force / (k * mass * radius)\n\nSubstituting the values:\n\nForce = 16 N\nk = 0.4\nMass = 2 kg\nRadius = 69 cm\n\nWe find that the angular acceleration of the solid sphere is approximately 29.0 rad/s\u00b2."
    },
    {
        "instruction": "A convex mirror produces 95 times diminished real image of an object at a distance of 42 cm from the mirror. At what distance is the object placed in front of the mirror?",
        "input": "Formula: u = v * n",
        "output": "To find the distance at which the object is placed in front of the mirror, we use the formula u = v * n, where u is the distance of the object from the mirror, v is the distance of the image from the mirror, and n is the magnification factor. By substituting the given values into the formula, we can calculate u. In this case, the object is placed at a distance of 3990 cm in front of the mirror., this is the final The object is placed at a distance of 3990 cm in front of the mirror."
    },
    {
        "instruction": "What is the lowest total resistance that can be secured by combinations of three coils of resistance 13, 88, 20?",
        "input": "R_total = (R1 * R2 * R3) / (R1 * R2 + R2 * R3 + R3 * R1)",
        "output": "The lowest combination of resistances can be obtained by connecting them in parallel. The total resistance is calculated as (13 * 88 * 20) / (13 * 88 + 88 * 20 + 20 * 13) = 7.2 ohm.\n\nTo calculate the lowest combination of resistances, we connect them in parallel. The total resistance (R_total) is given by the formula (R1 * R2 * R3) / (R1 * R2 + R2 * R3 + R3 * R1), where R1, R2, and R3 are the individual resistances."
    },
    {
        "instruction": "What is the gravitational potential at a point P at a distance of 324 m from the center of the spherical shell of radius 407 m and mass 230 kg?",
        "input": "Gravitational Potential (V) = cal1(230, 324, 407) joule/kg",
        "output": "The gravitational potential at a point P at a distance of 324 m from the center of the spherical shell of radius 407 m and mass 230 kg is given by the formula V = (-G * m) / R, where G is the gravitational constant, m is the mass, and R is the distance. Plugging in the values, we get V = -3.77e-11 joule/kg."
    },
    {
        "instruction": "A solid cylinder of radius 409 m weighs 14 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 37 m/s. How much work has to be done to stop it?\n",
        "input": "0.5*(0.5+1)*m*v*v",
        "output": "19166.0 joules\n"
    },
    {
        "instruction": "A bat emits ultrasonic sound of frequency 1334966 Hz in air. If this sound meets a water surface, what is the wavelength of the reflected sound? (Speed of sound in air = 340 ms-1 and in water = 1486 ms-1)\n",
        "input": "wavelength of refracted sound = speed of sound in air/frequency of the ultrasonic sound",
        "output": "2.55e-04 m\nGiven that the speed of sound in air is 340 m/s and the speed of sound in water is 1486 m/s, we can substitute these values into the formula to calculate the wavelength. For the sound emitted in air: \u03bb_air = (340 m/s) / 1334966 Hz, For the sound reflected in water: \u03bb_water = (1486 m/s) / 1334966 Hz"
    },
    {
        "instruction": "A disc revolves with a speed of 14 rpm and has a radius of 1 m. Two coins are placed at 34 cm (coin-1) and 61 cm (coin-2) away from the center of the record. If the coefficient of friction between the coins and the record is 0.8, which of the coins will revolve with the record?",
        "input": "Centripetal acceleration (a) = (\u03c0 / 30) * rot_speed\nOptimal radius (r_opt) = ((\u03bc * g) / (w * w)) * 100",
        "output": "coin1 will revolve,coin2 will revolve"
    },
    {
        "instruction": "9 capacitors each of capacitance 348pF are connected in series. What is the total capacitance of the combination when the system is connected to a 151 V supply?\n",
        "input": "1 / C_total = 1 / C1 + 1 / C2 + 1 / C3 + ... + 1 / Cn\n",
        "output": "3.87e+01 pico-farad\n\nExplanation: 1 / C_total = 1 / 348 + 1 / 348 + 1 / 348 + ... + 1 / 348\n"
    },
    {
        "instruction": "A monkey of mass 49 kg climbs on a rope which can stand a maximum tension of 138 N. In which of the following cases will the rope break: the monkey\n(a) climbs up with an acceleration of 9 ms-2\n(b) climbs down with an acceleration of 5 ms-2\n(c) climbs up (or) down with a uniform speed of 2 ms-1\n",
        "input": "Tension = m * (10 + 9)\nTension = m * (10 - 5)\nTension = m * 10",
        "output": "(a) break, (b) break, (c) break"
    },
    {
        "instruction": "Estimate the mean free path of a gas molecule in a cylinder containing gas at 48 atm and temperature 15 degree C. Take the radius of a gas molecule to be roughly 48 A.",
        "input": "mean_free_path = 1 / (sqrt(2) * pi * nu * (4 * r * r))",
        "output": "0.0 m\nHere, nu = (n * p) / (R * t1) = (6.022999999999999e+23 * 48 * 10^5) / (8.31 * 15 + 273) = 1.2079823505816284e+27\nmean_free_path = 1 / (sqrt(2) * pi * 1.2079823505816284e+27 * (4 * 48 * 10^-10 * 48 * 10^-10)) = 0.0"
    },
    {
        "instruction": "A rod of mass 3558 kg has a length of 42 m. What is the moment of inertia with respect to its end?",
        "input": "Moment of Inertia = (Constant) * mass * length^2",
        "output": "The moment of inertia with respect to its end is approximately 2092104.0 kgm^2.\n\nMoment of Inertia = (Constant) * mass * length^2\n\nConstant = 0.3333333333333333\nmass = 3558 kg\nlength = 42 m"
    },
    {
        "instruction": "In a process, 9238 J of heat is absorbed by the system and caused a change of -5754 J in internal energy of the system, what is the work done by the system ?\n",
        "input": "\u0394U = Q+W",
        "output": "from first law of thermodynamics, du = q + w => w = du - q => w = (-5754) - (-9238) => w = 3484joule\n"
    },
    {
        "instruction": "What is the side of a cube of volume 1320.042 cm3 (in m).\n",
        "input": "Volume = side^3",
        "output": "10969729\nCube of the side is it's volume."
    },
    {
        "instruction": "The transverse displacement of a string is given by y(x, t) = 0.27 sin 2\u03c0 /7 x cos (135\u03c0 t) where x, y are in m and t in s. The length of the string is 3 m and its mass is 0.1 kg,interpret this wave as a superimposition of two waves travelling in opposite direction, give  magnitude of speed of propagation of each wave?\n",
        "input": "speed = frequency*wavelength",
        "output": "9.6 ms-1\n"
    },
    {
        "instruction": "A bullet fired at an angle of 17 degrees with the horizontal hits the ground 441 m away. By adjusting its angle of projection, can one hope to hit a target 1582 m away?",
        "input": "no",
        "output": "The target is too far away to be hit."
    },
    {
        "instruction": "A copper wire has a cross-sectional area of 25 m\u00b2 and resistivity of 31 ohm-m. What is the length of this wire that makes its resistance 98 ohm?",
        "input": "R = 98 ohm, A = 25 m\u00b2, rho = 31 ohm-m",
        "output": "The length of the wire required to achieve a resistance of 98 ohm is 79.0 m. It is calculated by dividing the product of resistance and area (2450) by the resistivity (31)."
    },
    {
        "instruction": "A series LCR circuit is connected to a variable frequency 230 V source with L = 147 H, C = 110 muF, R = 194 ohm. Determine the RMS potential drop across capacitance?",
        "input": "RMS Potential Drop across Capacitance = Current RMS * 1 / (\u03c9_r * C)",
        "output": "RMS Potential Drop across Capacitance = 1.37e+03 V"
    },
    {
        "instruction": "Find the focal length of a concave mirror whose radius of curvature is 9680.7 cm.",
        "input": "Formula: f = R/2",
        "output": "To find the focal length of a concave mirror, we use the formula f = R/2, where f is the focal length and R is the radius of curvature. By substituting the given value of R into the formula, we can solve for f. In this case, the focal length is 4840.4 cm., this is the final 4840.4"
    },
    {
        "instruction": "The number of silicon atoms per m3 is 14 x 10^28. This is doped simultaneously with 13 x 10^(22) atoms per m3 of Arsenic and 2 x 10^20 atoms per m3 of Indium. Given that the ni = 833 x 10^16 m^(-3), calculate the number of protons, is it p-type or n-type?\n",
        "input": "Nh = Nh + N2 + N3",
        "output": "5.34e+14, n-type semiconductor\nThe total number of protons (Ne) is the sum of the number of holes (Nh) and the electrons contributed by the dopants.\n As the major dopant is Arsenic, it is a n-type semiconductor"
    },
    {
        "instruction": "Which uses more energy, a 7 W TV set in 70 s, or a 16 W toaster in 76 s?",
        "input": "",
        "output": "None, this is the final answer toaster"
    },
    {
        "instruction": "What is the gravitational potential at a point P at a distance of 161 m from a mass of 362 kg?",
        "input": "Gravitational Potential (V) = cal3(362, 161) joule/kg",
        "output": "The gravitational potential at a point P at a distance of 161 m from a mass of 362 kg is given by the formula V = (-G * m) / r, where G is the gravitational constant, m is the mass, and r is the distance. Plugging in the values, we get V = -1.50e-10 joule/kg."
    },
    {
        "instruction": "A solid sphere of radius 69 m weighs 75 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 24 m/s. How much work has to be done to stop it?\n",
        "input": "0.5*(0.4+1)*m*v*v",
        "output": "30240.0 joules\n"
    },
    {
        "instruction": "A small bulb is placed at the bottom of a tank containing liquid to a depth of 221 cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of the liquid is 1.84.",
        "input": "Formula: Area = \u03c0 * h\u00b2 * (k / (1 - k)), where h is the depth of the liquid in centimeters, k is the reciprocal of the refractive index of the liquid, and k = 1 / mu.",
        "output": "This is the answer 6.43 m\u00b2, formula used is : Formula: Area = \u03c0 * h\u00b2 * (k / (1 - k)), where h is the depth of the liquid in centimeters, k is the reciprocal of the refractive index of the liquid, and k = 1 / mu."
    },
    {
        "instruction": "Torque of 500 Nm is transmitted to an engine at a power of 866 W. What is the angular speed of the rotor?",
        "input": "Angular Speed = Power / Torque",
        "output": "Angular Speed = 866 W / 500 Nm\n\nTo calculate the angular speed of the rotor, we use the following formula:\n\nAngular Speed = Power / Torque\n\nSubstituting the values:\n\nPower = 866 W\nTorque = 500 Nm\n\nWe find that the angular speed of the rotor is 1.7 rad/s."
    },
    {
        "instruction": "A bat is flitting about in a cave, navigating via ultrasonic beeps. Assume that the sound emission frequency of the bat is 33740 Hz. During one fast swoop directly toward a flat wall surface, the bat is moving at 0.0664 times the speed of sound in air. What frequency does the bat hear reflected off the wall?\n",
        "input": "apparent frequency = [{(speed of air + speed of bat)}/speed of air]*apparent frequency of sound striking the wall",
        "output": "3.85e+04 hertz\nThe concept of Doppler's effect has been applied to calculate apparent frequencies."
    },
    {
        "instruction": "A wire made up of unknown material has a resistance 118 ohm at 162 degree C, and a resistance of 132 ohm at 178 degree C. Determine the temperature coefficient of resistivity of that material?",
        "input": "temp_coeff = (R2 - R1) / (R1 * T2)",
        "output": "7.42e-03 degree centigrade-1\n\nTo determine the temperature coefficient of resistivity, use the formula: temp_coeff = (R2 - R1) / (R1 * T2), where R2 is the final resistance, R1 is the initial resistance, T2 is the temperature change, and temp_coeff is the temperature coefficient."
    },
    {
        "instruction": "An image is formed by a concave mirror of focal length 837 cm at a distance of 536 cm behind it. Find at what distance object is placed in front of mirror.",
        "input": "Formula: 1/f = 1/v + 1/u",
        "output": "To find the distance of the object, we use the formula 1/f = 1/v + 1/u, where f is the focal length, v is the distance of the image, and u is the distance of the object. By substituting the given values into the formula, we can solve for u. In this case, the distance of the object is 326.8 cm., this is the final 326.8"
    },
    {
        "instruction": "For a CE-transistor amplifier, the audio signal voltage across the collected resistance of 2460 ohm is 23 V. Suppose the current amplification factor of the transistor is 60, find the input signal voltage if the base resistance is 1840 ohm?\n",
        "input": "output voltage/input voltage = current amplification factor*output resistance/input resistance",
        "output": "voltage without amplification is 23/60 = 0.38, to get voltage per unit resistance, we need to divide it by 2460, to get to original voltage, we need to multiply per unit resistance voltage with base resistance 1840 doing all that we get, 2.87e-01 volt\n"
    },
    {
        "instruction": "A long straight wire in the horizontal plane carries a current of of 190 A in south to north direction. What is the magnitude and direction of the magnetic field B at a point 125 cm west of the wire.\n",
        "input": "B = (mu * i) / (2 * pi * r)",
        "output": "To calculate the magnitude and direction of the magnetic field B, we use the following formula:\n\nB = (mu * i) / (2 * pi * r)\n\nWhere,\n- B = Magnetic field\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- i = Current flowing through the wire\n- r = Distance from the wire\n\nSubstituting the given values into the formula, we find that the magnitude and direction of the magnetic field B is approximately 3.0e-05 tesla vertically upwards\n."
    },
    {
        "instruction": "A wire of material-1 of length 115 m and cross-sectional area 8 x 10^(-6) m^2 stretches by the same amount as a wire of material-2 of length 30 m and cross-sectional area 4 x 10^(-6) m^2 under a given load. What is the ratio of the Young\u2019s modulus of material-1 to that of material-2?",
        "input": "ratio = (l1 * A2) / (l2 * A1)",
        "output": "The ratio of the Young's modulus of material-1 to that of material-2 is approximately 1.92. To calculate the ratio, we use the formula:\n\nratio = (l1 * A2) / (l2 * A1)"
    },
    {
        "instruction": "A bike starting with an initial velocity of 489 m/s travels on a straight road at a constant rate of 65 m/s\u00b2 for 5 s. How far does the bike travel during this time?",
        "input": "initial velocity (u) = 489 m/s, acceleration (a) = 65 m/s\u00b2, time (t) = 5 s",
        "output": "3257.5 m \n\ndistance (s) = initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)\u00b2\ns = 489 * 5 + 0.5 * 65 * 5\u00b2\ns = 2445 + 812.5\ns = 3257.5"
    },
    {
        "instruction": "Two trains A and B of length 55 m each are moving on two parallel tracks with a uniform speed of 96 m/s in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by 1 m/s\u00b2. If after 20 s, the guard of B just brushes past the driver of A, what was the original distance between them?",
        "input": "separation distance = (1 / 2) * acceleration * (time ** 2)",
        "output": "acceleration of B is 1 m/s\u00b2, time taken by B to cover the separation distance is 20 s, length of each train is 55 m, speed of each train is 96 m/sThe original distance between the two trains is 90.0 m.\n\nseparation distance = (1 / 2) * acceleration * (time ** 2)\n\nThe separation distance between the two trains is the distance covered by the guard of B in the time interval of 20 s. The guard of B covers this distance in the time interval of 20 s with an acceleration of 1 m/s\u00b2. The original distance between the two trains is the separation distance minus the sum of the lengths of the two trains."
    },
    {
        "instruction": "A tank is filled with water to a height of 91.6 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 82.0 cm. What is the refractive index of water?",
        "input": "Formula: refractive index = height of tank / apparent depth of needle",
        "output": "To calculate the refractive index, we use the formula: refractive index = height of tank / apparent depth of needle. In this case, the height of the tank is 91.6 cm and the apparent depth of the needle is 82.0 cm., this is the final 1.12"
    },
    {
        "instruction": "A 31 pF capacitor is charged by a 142 V supply. It is then disconnected from the supply and is connected to another uncharged 103 pF capacitor. How much electrostatic energy is lost in this process?",
        "input": "Formula: (312542.0 - 240237.50746268657) * 10^(-12)\nValues: c1 = 31 pF, c2 = 103 pF, v = 142 V",
        "output": "Answer:7.23e-08 joule\n\nExplanation: The electrostatic energy lost in the process can be calculated by subtracting the final energy from the initial energy:\n\nE_loss = E_initial - E_final\n\nThe initial energy E_initial can be calculated as 0.5 * C1 * V^2, where C1 is the capacitance of the first capacitor and V is the voltage. The final energy E_final can be calculated as 0.5 * C3 * V^2, where C3 is the equivalent capacitance when the two capacitors are combined.\n\nSubstituting the given values, we have:\n\nE_loss = 312542.0 joule - 240237.50746268657 joule = E_loss = 7.23e-08 joule joule."
    },
    {
        "instruction": "An image is formed by a concave lens of focal length 868 cm at a distance of 137 cm behind it. Find at what distance object is placed in front of lens.",
        "input": "Formula: 1/f = 1/v - 1/u for concave lens.",
        "output": "This is the answer The object is placed at 163 cm in front of the lens., formula used is : Formula: 1/f = 1/v - 1/u for concave lens."
    },
    {
        "instruction": "An object moving with a speed of 932 kmph covers x m in 668 s, then find the value of x?\n",
        "input": "Distance = Speed*Time",
        "output": "172937.8\nDistance = Speed*Time"
    },
    {
        "instruction": "A pair of adjacent coils has a mutual inductance of 6.9 H. If the current in one coil changes from 21 A to 8 A in 1.0 sec, what is the change of flux linkage with the other coil?\n",
        "input": "Change in Flux Linkage = (Mutual Inductance * (Current 1 - Current 2)) / Time",
        "output": "89.7 weber\n\n\nThe change of flux linkage with the other coil can be calculated using the formula Change in Flux Linkage = (Mutual Inductance * (Current 1 - Current 2)) / Time, where Mutual Inductance is the mutual inductance of the coils, Current 1 and Current 2 are the initial and final currents respectively, and Time is the time taken for the change in current to occur."
    },
    {
        "instruction": "A circular coil of wire consisting of 65 turns, each of radius 283 cm carries a current of 19 A. What is the magnitude of the magnetic field B at the center of the coil?",
        "input": "B = (mu * n * i) / (2 * r)",
        "output": "To calculate the magnetic field B at the center of the coil, we use the following formula:\n\nB = (mu * n * i) / (2 * r)\n\nWhere,\n- B = Magnetic field at the center of the coil\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- n = Number of turns in the coil\n- i = Current flowing through the coil\n- r = Radius of the coil\n\nSubstituting the given values into the formula, we find that the magnitude of the magnetic field B is approximately 2.74e-04 tesla."
    },
    {
        "instruction": "Suppose that the electric field amplitude of an electromagnetic wave is E0 = 1465 N/C and that its frequency is v = 481 MHz. Find an expression for B?",
        "input": "B0 = 4.88e-06 tesla, k = 1.01e+01 rad/m, w = 3.02e+09 rad/s",
        "output": "4.88e-06sin[1.01e+01x-3.02e+09t]\n\nThe expression for the magnetic field (B) of an electromagnetic wave can be written as B = B0sin(kx - wt)."
    },
    {
        "instruction": "A TV antenna is 14433 cm tall. How much service area can it cover if the receiving antenna is at ground level?",
        "input": "Service_area = pi * 2 * 6.4 * 10000 * l",
        "output": "5.80e+09 m2"
    },
    {
        "instruction": "Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapor, and other constituents) in a room of capacity 58 m3 at a temperature of 46 degree C and 88 atm pressure.",
        "input": "total_number_of_molecules = (p * v) / (k * t1)",
        "output": "1.1594202898550726e+29 molecules\nHere, p = 88 atm = 8800000 Pa, v = 58 m3, t1 = 46 degree C = 319 K, k = 1.38 x 10^-23 J/K"
    },
    {
        "instruction": "Calculate the charge (in C) of 9.82e+18 electrons?",
        "input": "Q = n * e",
        "output": "1.60e+00 coulomb\n\nThe charge of electrons can be calculated using the formula: Q = n * e, where n is the number of electrons and e is the charge of an electron."
    },
    {
        "instruction": "An aircraft of mass 46 kg executes a horizontal loop at a speed of 161 m/s with its wings banked at 5 degrees. What is the radius of the loop?",
        "input": "(v^2) / (g * tan((param * pi) / 180))",
        "output": "29628\nTo calculate the radius, we use the formula (v^2) / (g * tan((param * pi) / 180)), where v is the speed (161 m/s), g is the acceleration due to gravity (10 m/s^2), and param is the angle of banking (5 degrees)."
    },
    {
        "instruction": "A end of string of mu = 0.015 kgm-1 is connected to tuning fork of nu = 340 Hz. The other end passes over a pulley and is tied to a mass of 100 kg. The pulley end is such that reflected waves at this end have negligible amplitude. At t = 0, the fork end of the string x = 0 has y = 0 and is moving along +ve y axis. The amplitude of the wave is 18 cm. Write down y as function of x,t that describes the wave on the string.\n",
        "input": "wavelength = speed/frequency",
        "output": "0.18 sin(1.6e+03t - 8.4e+00x)\nto form wave equation, we have to find amplitude, frequency, velocity of wave. given, amplitude = 18 cm = 0.18 m ,frequency = 340 hz ,v = sqrt(t/mu) = sqrt(980.0/0.015) = 255.6 ,w = 2*pi*v = 2*3.14*255.6 = 1606.0 ,wavelength = v/freq = 255.6/340 ,k = 2*pi/wavelength =  2*pi*340/255.6 = 8.4 ,the equation of the wave is, v(x,t) = a sin(wt-kx), "
    },
    {
        "instruction": "Suppose that the electric field part of an electromagnetic wave in vacuum is E = 1540cos[739y + 405954t]. What is the wavelength?",
        "input": "k = 739",
        "output": "8.50e-03 m\n\nThe wavelength can be calculated by dividing 2\u03c0 by the wave number (k)."
    },
    {
        "instruction": "To maintain a rotor at a uniform angular speed of 117 rad/s, an engine needs to transmit a torque of 360 Nm. What is the power required by the engine?",
        "input": "Power = Angular Speed * Torque",
        "output": "Power = 117 rad/s * 360 Nm\n\nTo calculate the power required by the engine, we use the following formula:\n\nPower = Angular Speed * Torque\n\nSubstituting the values:\n\nAngular Speed = 117 rad/s\nTorque = 360 Nm\n\nWe find that the power required by the engine is 42120 watts."
    },
    {
        "instruction": "A small town with a demand of 980 kW of electric power at 220 V is situated 25 km away from an electric plant generating power at 440 V. The resistance of each of the two wires carrying power is 0.74 ohm per km. The town gets power from the line through 3350 - 220 V step down transformer at a sub-station in the town. Characterize the step-up transformer at the plant.",
        "input": "Voltage_Drop = I * resistance_drop * 2 * distance\nStep_up_transformer_rating = Bigger_voltage - Voltage_drop",
        "output": "rating is 440 volt -- 1.42e+04 volt"
    },
    {
        "instruction": "For a CE-transistor amplifier, the audio signal voltage across the collected resistance of 2970 ohm is 34 V. Suppose the current amplification factor of the transistor is 150, find the input signal voltage if the base resistance is 1990 ohm?\n",
        "input": "output voltage/input voltage = current amplification factor*output resistance/input resistance",
        "output": "voltage without amplification is 34/150 = 0.23, to get voltage per unit resistance, we need to divide it by 2970, to get to original voltage, we need to multiply per unit resistance voltage with base resistance 1990 doing all that we get, 1.52e-01 volt\n"
    },
    {
        "instruction": "Earthquakes generate sound waves inside the earth, assuming the speed of transverse(S) wave is 5850 ms-1, speed of longitudinal(P) wave is 6100 ms-1, if the first P wave arrives 374 s before the first S wave to seismograph, at what distance does the earthquake occur?\n",
        "input": "Vs*Ts=Vp*Tp, L = Vp*Tp",
        "output": "5.34e+04 km\nTo determine the distance to the earthquake epicenter, we can use the difference in arrival times between the P wave and S wave at the seismograph.Using the formula for distance (d) based on wave speed and time: d = (P wave speed - S wave speed) * t"
    },
    {
        "instruction": "A end of string of mu = 0.022 kgm-1 is connected to tuning fork of nu = 280 Hz. The other end passes over a pulley and is tied to a mass of 95 kg. The pulley end is such that reflected waves at this end have negligible amplitude. At t = 0, the fork end of the string x = 0 has y = 0 and is moving along +ve y axis. The amplitude of the wave is 2 cm. Write down y as function of x,t that describes the wave on the string.\n",
        "input": "wavelength = speed/frequency",
        "output": "0.02 sin(1.3e+03t - 8.6e+00x)\nto form wave equation, we have to find amplitude, frequency, velocity of wave. given, amplitude = 2 cm = 0.02 m ,frequency = 280 hz ,v = sqrt(t/mu) = sqrt(931.0/0.022) = 205.7 ,w = 2*pi*v = 2*3.14*205.7 = 1292.5 ,wavelength = v/freq = 205.7/280 ,k = 2*pi/wavelength =  2*pi*280/205.7 = 8.6 ,the equation of the wave is, v(x,t) = a sin(wt-kx), "
    },
    {
        "instruction": "A SONAR system fixed in a submarine operates at a frequency 88620 Hz. An enemy submarine moves towards the SONAR with a speed of 351 kmph. What is the frequency of sound reflected by the submarine? Take the speed of sound in water to be 1450 ms-1.\n",
        "input": "Apparent frequency = [(Speed of sound in air + Speed of enemy submarine)/Speed of sound in air]*Original Frequency",
        "output": "1.01e+05 hertz\nTo calculate the frequency of sound reflected by the submarine in the SONAR system, we need to consider the Doppler effect due to the relative motion between the submarines. The Doppler effect accounts for the change in frequency observed when the source of sound and the observer are in relative motion.The formula to calculate the frequency observed by the submarine is: f' = f * (v_sound / (v_sound - v_sub)), where f' is the observed frequency, f is the emitted frequency, v_sound is the speed of sound in water, and v_sub is the velocity of the submarine."
    },
    {
        "instruction": "A spring balance has a scale that reads from 0 to 135 kg. The length of the scale is 175 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 735 ms. What is the weight of the body?",
        "input": "Formula: w = (t^2 * k) / (4 * \u03c0^2), where w is the weight of the body, t is the period of oscillation (735 ms), and k is the spring constant given by (m * g) / (l * 0.01), where m is the reading on the scale (135 kg), g is the acceleration due to gravity (9.8 m/s^2), and l is the length of the scale (175 cm).",
        "output": "Using this formula: Formula: w = (t^2 * k) / (4 * \u03c0^2), where w is the weight of the body, t is the period of oscillation (735 ms), and k is the spring constant given by (m * g) / (l * 0.01), where m is the reading on the scale (135 kg), g is the acceleration due to gravity (9.8 m/s^2), and l is the length of the scale (175 cm)., this is the final answer derived: The spring constant k can be found out using the maximum mass and length of the scale as k = (m * g) / (l * 0.01), which is (135 * 9.8) / (1.75) = 756.0.\nWe know that the time period of simple harmonic motion is given by t = 2\u03c0\u221a(m / k). From this equation, we can rearrange it to solve for m: m = (t^2 * k) / (4\u03c0^2).\nMultiplying the resulting mass with g, we get the weight, which is equal to (735^2 * 756.0) / (4\u03c0^2) = 1.01e+02 newton."
    },
    {
        "instruction": "For an amplitude modulated wave, the maximum amplitude is found to be 7.19 V while the minimum amplitude is found to be 5.22 V. Determine the modulation index.\n",
        "input": "Modulation index = (a_max - a_min) / (a_max + a_min)",
        "output": "We know that the modulation index of an amplitude modulated wave is the ratio of the difference between a_max and a_min to the sum of a_max and a_min. The difference of a_max, a_min is equal to 7.19 - 5.22 = 1.97, and the sum of a_max, a_min is equal to 7.19 + 5.22 = 12.41. Hence, the modulation index is equal to 1.97 / 12.41 = 0.16\n"
    },
    {
        "instruction": "A steel rod 1377 cm long is hinged at its middle. The fundamental frequency of longitudinal vibrations of the rod is given to be 2127 Hz. What is the speed of sound in steel?\n",
        "input": "speed of sound in steel = frequency*wavelength",
        "output": "5.9e+04 ms-1\nThe distance between two successive nodes is wavelength/2."
    },
    {
        "instruction": "A 40 muF capacitor in series with a 45 ohm resistance is connected to a 226 V, 49 Hz supply. What is the time lag between the current maximum and voltage maximum?",
        "input": "Time_lag = atan(1 / (f * C * 10^-6 * 2 * pi * R)) / (2 * pi * f)",
        "output": "3.46e-03 s"
    },
    {
        "instruction": "An Electric bulb draws current from the service mains of potential difference 89 V and produces heat at 185 W for 95 s. Calculate the resistance of the bulb?",
        "input": "R = (V * V) / P",
        "output": "42.8 ohm\n\nThe resistance of the bulb can be calculated using the formula: R = (V * V) / P, where V is the potential difference and P is the power."
    },
    {
        "instruction": "If a monoatomic gas of 2 moles at 83 atm and volume 135 lit is adiabatically changed to volume 171 lit, then what will be the pressure.\n",
        "input": "P1*(V1^1.66)=P2*(V2^1.66)",
        "output": "56.1atm\nTo calculate the final pressure of the monoatomic gas after an adiabatic expansion, we can use the adiabatic equation: P1 * V1^\u03b3 = P2 * V2^\u03b3, where P1 and V1 are the initial pressure and volume, P2 and V2 are the final pressure and volume, and \u03b3 is the heat capacity ratio. The heat capacity ratio (\u03b3) for a monoatomic gas is typically 5/3."
    },
    {
        "instruction": "If current flowing through a conductor is 862 A, then what is the charge flown through the conductor in 847 s?",
        "input": "Q = I * t",
        "output": "7.30e+05 coulomb\n\nThe charge flown through the conductor can be calculated using the formula: Q = I * t, where I is the current and t is the time."
    },
    {
        "instruction": "A hollow sphere of mass 6070 kg has a radius of 2 m. What is the moment of inertia with respect to its symmetric axis?",
        "input": "Moment of Inertia = (Constant) * mass * radius^2",
        "output": "The moment of inertia with respect to its symmetric axis is approximately 16186.7 kgm^2.\n\nMoment of Inertia = (Constant) * mass * radius^2\n\nConstant = 0.6666666666666666\nmass = 6070 kg\nradius = 2 m"
    },
    {
        "instruction": "A 133 mH inductor is connected to 26 V, 182 Hz ac supply. Determine the rms value of current in the circuit?",
        "input": "X_l = 2 * pi * f * L * 0.001\nI_rms = V / X_l",
        "output": "1.71e-01 ampere"
    },
    {
        "instruction": "A wheel starting with an initial angular velocity of 41 rad/s is applied with a constant angular acceleration of 1 rad/s\u00b2. What is the time taken to reach an angular position of 929 rad?",
        "input": "time = (-(2 * initial_angular_velocity) + sqrt((4 * initial_angular_velocity^2) + (8 * angular_acceleration * angular_position))) / (2 * angular_acceleration)",
        "output": "To calculate the time, we use the following formula:\n\ntime = (-(2 * initial_angular_velocity) + sqrt((4 * initial_angular_velocity^2) + (8 * angular_acceleration * angular_position))) / (2 * angular_acceleration)\n\nSubstituting the given values into the formula, we find that the time is approximately 18.5 seconds."
    },
    {
        "instruction": "A particle of mass 200 g and charge -(2) C enters a region between two charged particles initially moving along the x-axis with speed 7 m/s. The length of plates is 16 cm, and a uniform electric field of 10 N/C is applied. Find the vertical deflection?\n",
        "input": "Vertical Deflection Formula: vertical_deflection = (q1 * E * L^2 * 0.0001) / (m * v^2 * 0.001)\n",
        "output": "5.22e-02 m\n"
    },
    {
        "instruction": "A 169 kg mass, fastened to the end of a steel wire of initial length 38 m, is whirled in a vertical circle with an angular velocity of 7 rev/s at the bottom of the circle. The cross-sectional area of the wire is 86 mm^2. Calculate the elongation of the wire when the mass is at the lowest point of its path.",
        "input": "elongation = (force * length) / (A * 10^(-6) * Y_steel)",
        "output": "To calculate the elongation, we use the formula:\n\nelongation = (force * length) / (A * 10^(-6) * Y_steel)\n = (169 kg * (9.8 + 38 m * \u03c0^2 * 7^2) * 38 m) / (86 mm^2 * 10^(-6) m^2 * (2 * 10^11 N/m^2))\n = 686.5 cm."
    },
    {
        "instruction": "A toroid has a core of inner radius 62 cm and outer radius 110 cm, around which 257 turns of a wire are wound. If the current in the wire is 49 A, what is the magnetic field inside the core of the solenoid.",
        "input": "Magnetic field = (mu * n * i) / l",
        "output": "To calculate the magnetic field inside the toroid, we use the following formula:\n\nMagnetic field = (mu * n * i) / l\n\nWhere,\n- n = Number of turns of the wire\n- i = Current in the wire\n- l = Length of the wire\n\nWe calculate the length of the wire using the formula:\n- Length of the wire = (r1 + r2) * pi\n\nSubstituting the given values and evaluating the formula, we find that the magnetic field inside the core of the toroid is approximately 2.93e-03 tesla."
    },
    {
        "instruction": "Two point charges q1 = -69 x 10^(-6)C and q2 = -42 x 10^(-6)C are located 71 cm apart in vacuum. What is the force on the test charge of 3 x 10^(-6)C placed at the midpoint of the line joining two charges?\n",
        "input": "Electric field = (q1 - q2) / (4 * pi * epsilon * r^2)\nForce = Electric field * test charge",
        "output": "To calculate the force on the test charge at the midpoint, we use the formula:\nForce = Electric field * test charge\nGiven the electric field as calculated before and the test charge qmid = 3 x 10^(-6)C,\nForce = 5.78e+00 newton\n"
    },
    {
        "instruction": "To maintain a rotor at a uniform angular speed of 215 rad/s, an engine requires a power of 370 W. What is the torque transmitted by the engine?",
        "input": "Torque = Power / Angular Speed",
        "output": "Torque = 370 W / 215 rad/s\n\nTo calculate the torque transmitted by the engine, we use the following formula:\n\nTorque = Power / Angular Speed\n\nSubstituting the values:\n\nPower = 370 W\nAngular Speed = 215 rad/s\n\nWe find that the torque transmitted by the engine is 1.7 Nm."
    },
    {
        "instruction": "What is the focal length of a system of convex lens of focal length 4 cm, a concave lens of focal length 27 cm, and a concave lens of focal length 20 cm? Is the system a converging or a diverging lens? Ignore thickness of the lenses.",
        "input": "Formula: For a system of three lenses, the combined focal length (P) is given by P = (f1 * f2 * f3) / (f1 * f2 + f2 * f3 + f3 * f1), where f1, f2, and f3 are the focal lengths of the lenses.",
        "output": "This is the answer {answer}, formula used is : {formula}"
    },
    {
        "instruction": "Two point charges q1 = -57 x 10^(-6)C and q2 = 40 x 10^(-6)C are located 28 cm apart in vacuum. What is the electric field at the midpoint O of the line joining two charges?\n",
        "input": "Electric field = (q1 - q2) / (4 * pi * epsilon * r^2)",
        "output": "To calculate the electric field at the midpoint O, we use the formula:\nElectric field = (q1 - q2) / (4 * pi * epsilon * r^2)\nGiven q1 = -57 x 10^(-6)C, q2 = 40 x 10^(-6)C, and r = 28 cm,\nElectric field = 4.45e+07 newton/coulomb\n"
    },
    {
        "instruction": "Number of significant digits in 0.0006951847000\n",
        "input": "",
        "output": "3 zeros after the decimal point to the left of first non zero digit are not significant, 7 digits(which start and end with non zero digit) in between are significant, 3 digits to the right of last non-zero digits are significant(as they are after decimal point), in total 7 + 3 = 10 digits are significant.\n"
    },
    {
        "instruction": "A force of 617 N acts on an object causes displacement in the direction of the force. If work done is equal to 9517 J, then what is the displacement?",
        "input": "s = W / F",
        "output": "Using the formula: s = W / F, the final answer is: {'answer': '15.4 m', 'explanation': 'To calculate the displacement, we use the formula s = W / F, where s is the displacement, W is the work done (9517 J), and F is the force (617 N).'}"
    },
    {
        "instruction": "A body is dropped from a height of 8825 m and reaches the ground with a velocity of 173020 m/s. With what initial velocity was it dropped?",
        "input": "height (h) = 8825 m, final velocity (v) = 173020 m/s",
        "output": "initial velocity (u) = \u221a(final velocity (v)\u00b2 - 2 * acceleration (g) * height (h))\nu = \u221a(173020\u00b2 - 2 * 9.8 * 8825)\nu = \u221a(29935920400 - 172970.0)\nu = \u221a29935747430.0\nu = \u221a173019.5\nu = 173019.5"
    },
    {
        "instruction": "A parallel plate capacitor made of circular plates of radius r = 131 cm has a capacitance C = 143 pF. The capacitor is connected to a 230 V ac supply with an angular frequency of 550 rad/s. What is the rms value of the conduction current?",
        "input": "I = 1.81e-05 ampere",
        "output": "1.81e-05 ampere\n\nThe rms value of the conduction current can be calculated by taking the square root of the average of the square of the current."
    },
    {
        "instruction": "A convex mirror produces 49 times diminished real image of an object placed at 3 cm in front of it. At what distance is the image formed from the mirror?",
        "input": "Formula: v = u / n",
        "output": "To find the distance at which the image is formed from the mirror, we use the formula v = u / n, where v is the distance of the image from the mirror, u is the distance of the object from the mirror, and n is the magnification factor. By substituting the given values into the formula, we can calculate v. In this case, the image is formed at a distance of 0.1 cm from the mirror., this is the final The image is formed at a distance of 0.1 cm from the mirror."
    },
    {
        "instruction": "Which of the following is the most precise device for measuring length: (a) a vernier callipers with 468 divisions on the sliding scale, (b) a screw guage of pitch 6 mm and 3929 divisions on the circular scale, (c) an optical instrument that can measure length to within a wavelength of light?\n",
        "input": "",
        "output": "(c)\nTo determine the most precise device for measuring length among the options given, we need to consider the number of divisions or increments on each device and the accuracy of the measurements they can provide, (a) Vernier Callipers: A vernier callipers typically consists of a main scale and a sliding scale with a vernier scale. The vernier scale allows for more precise measurements by providing additional divisions that correspond to a fraction of the main scale division. The precision of the vernier callipers depends on the number of divisions on the sliding scale. (b) Screw Gauge: A screw gauge measures small lengths based on the rotation of a screw with a known pitch. The pitch represents the distance moved per revolution of the screw. The precision of the screw gauge depends on the number of divisions on the circular scale. (c) Optical Instrument: An optical instrument that can measure length to within a wavelength of light has the potential for extremely high precision. The wavelength of light is typically in the order of nanometers, which allows for very accurate measurements. Comparing the options, the optical instrument that can measure length to within a wavelength of light offers the highest precision among the given choices. It can provide measurements with accuracy down to the scale of the wavelength of light."
    },
    {
        "instruction": "If a gas molecule has average velocity of 1919 m/s and is at a temperature 2 degree C. What is the molar mass of the gas. (R = 8.31 J/molK)",
        "input": "(3 * r * t1 * 1000) / (math.pi * v * v)",
        "output": "3.5038297647006122 m/s\n The formula used is: (3 * r * t1 * 1000) / (math.pi * v * v)"
    },
    {
        "instruction": "Two heavy spheres each of mass 45 kg, 96 kg respectively are placed 101 m apart on a horizontal table. What is the gravitational field at the mid point of the line joining the centres of the spheres? G = 6.67 x 10^-11",
        "input": "Gravitational Field (g) = 1.33e-12 newton/kg",
        "output": "The gravitational field at the mid point of the line joining the centres of the spheres is given by the formula g = (-1 * G * m1 / (R^2)) + (G * m2 / (R^2)), where G is the gravitational constant, m1 and m2 are the masses of the spheres, and R is the distance between them. Plugging in the values, we get g = 1.33e-12 N/kg."
    },
    {
        "instruction": "If a diatomic gas of 3 moles at 19 pas is isothermally changed to pressure 41 pas at 37 K, then what is the work done.\n",
        "input": "Work Done = n*R*T*ln(P1/P2)",
        "output": "709.5 joules\nTo calculate the work done during an isothermal expansion of a diatomic gas, we can use the following equation: Work done = n * R * T * ln(P1/P2), where n is the number of moles of the gas, R is the ideal gas constant (approximately 8.314 J/(mol\u00b7K)), T is the temperature in Kelvin, P1 is the initial pressure, and P2 is the final pressure."
    },
    {
        "instruction": "Suppose we employ a system of units in which the unit of mass equals 24 kg, the unit of length equals 77 m, the unit of time is 77 s, then value of 15 newton in new system\n",
        "input": "15 N = (m kg) * (l m) / (t^2 s^2)",
        "output": "48.13\nTo find the value of 15 newtons in the given system of units, we need to consider the relationships between the units of mass (kg), length (m), time (s), and force (Newton). In the new system of units, we have: 1 unit of mass = 48.13\n kg, 1 unit of length = 77 m, 1 unit of time = 77 s. To find the value of 15 newtons, we need to determine the conversion factors between the new system and the standard SI units. The force (Newton) can be expressed as: 15 N = (m kg) * (l m) / (t^2 s^2). Substituting the given values into this equation, we have: 15 N = (m * 48.13\n kg) * (l * 77 m) / (t^2 * 77 s^2). Simplifying this expression will give us the value of 15 newtons in the new system of units."
    },
    {
        "instruction": "A body is dropped from the top of a building with an initial velocity of 2830 m/s under gravity, and it reaches the ground after 164 s. What is the height of the building?",
        "input": "initial velocity (u) = 2830 m/s, time (t) = 164 s",
        "output": "height (s) = initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)\u00b2\ns = 2830 * 164 + 0.5 * 9.8 * 164\u00b2\ns = 464120 + 131790.40000000002\ns = 595910.4"
    },
    {
        "instruction": "If a wheel of radius 493 m has an angular acceleration of 336 rad/s\u00b2, what is the acceleration of a point at the circumference of the wheel?",
        "input": "acceleration_at_circumference = angular_acceleration * radius",
        "output": "To calculate the acceleration at the circumference, we use the following formula:\n\nacceleration_at_circumference = angular_acceleration * radius\n\nSubstituting the given values into the formula, we find that the acceleration at the circumference is approximately 165648 m/s\u00b2."
    },
    {
        "instruction": "A particle starts from origin at t = 0 s with a velocity of (7) i + (-1) j ms-1 and moves in x-y plane with a constant acceleration of (2) i + (-1) j ms-2, then what is the time taken to reach the final velocity of 23 i + -9 j ms-1",
        "input": "v = u + a * t",
        "output": "t = 8 s"
    },
    {
        "instruction": "A pump on the ground floor of a building can pump up water to fill a tank of volume 71 m3 in 15 min. If the tank is 20 m above the ground, and the efficiency of the pump is 68%, how much electric power is consumed by the pump?\n",
        "input": "(100000*v*h*9.8)/(t*e)",
        "output": "To find the electricity in the pump: (100000*v*h*9.8)/(t*e), this is the final answer 22738.56watts\n"
    },
    {
        "instruction": "If a diatomic gas of 8 moles at 49 atm and volume 135 lit is isothermally changed to volume 32 lit, then what will be the pressure.\n",
        "input": "P1*V1 = P2*V2",
        "output": "206.7atm\nTo determine the final pressure of a diatomic gas after an isothermal expansion, we can use Boyle's Law, which states that for an ideal gas at constant temperature: P1 * V1 = P2 * V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume."
    },
    {
        "instruction": "A hollow cylinder of radius 44 m weighs 99 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 24 m/s. How much work has to be done to stop it?\n",
        "input": "0.5*(1+1)*m*v*v",
        "output": "57024.0 joules\n"
    },
    {
        "instruction": "Two masses each of mass 29 kg are attached by a spring with K = 49 Nm-1. If a force of 109 N is applied at the free ends of both masses, then what is the time period of oscillation?",
        "input": "Formula: T = 2\u03c0\u221a(m / (2k)), where T is the time period of oscillation, m is the mass of each mass (29 kg), and k is the spring constant (49 Nm-1).",
        "output": "Using this formula: Formula: T = 2\u03c0\u221a(m / (2k)), where T is the time period of oscillation, m is the mass of each mass (29 kg), and k is the spring constant (49 Nm-1)., this is the final answer derived: 3.42e+00 s"
    },
    {
        "instruction": "An aircraft of mass 186 kg executes a horizontal loop at a speed of 349 m/s with its wings banked at 71 degrees. What is the radius of the loop?",
        "input": "(v^2) / (g * tan((param * pi) / 180))",
        "output": "4194\nTo calculate the radius, we use the formula (v^2) / (g * tan((param * pi) / 180)), where v is the speed (349 m/s), g is the acceleration due to gravity (10 m/s^2), and param is the angle of banking (71 degrees)."
    },
    {
        "instruction": "Two large thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude 1183966 x 10^(-22) C/m\u00b2. What is E: between the plates?\n",
        "input": "Electric field (E) = surface charge density / (2 * epsilon_0)",
        "output": "To calculate the electric field between the plates, we use the formula:\nElectric field (E) = surface charge density / (2 * epsilon_0)\nGiven surface charge density = 1183966 x 10^(-22) C/m\u00b2,\nElectric field (E) = 1.34e-05 N/C\n"
    },
    {
        "instruction": "Two lamps, one rated 54 W at 233 V, and the other 92 W at 220 V, which has more resistance?",
        "input": "",
        "output": "lamp1"
    },
    {
        "instruction": "A force is applied on a body of mass 733 kg placed on a smooth surface resulting in acceleration of 88 m/s^2, then what is the force applied?",
        "input": "F = m * a",
        "output": "64504\nTo calculate the force, we use the formula F = m * a, where F is the force, m is the mass (733 kg), and a is the acceleration (88 m/s^2)."
    },
    {
        "instruction": "A refrigerator is to maintain eatables kept inside at -88 degree C, if room temperature is 95 degree C. Calculate the coefficient of performance.\n",
        "input": "Coefficient of performance = T2/T1-T2",
        "output": "1.0\nThis formula is only applicable if the refrigerator is based on the Carnot Cycle."
    },
    {
        "instruction": "Calculate root mean square velocity of a gas molecule having molar mass of 363 g/mol at 631 degree C.",
        "input": "math.sqrt((3 * r * t1 * 1000) / m)",
        "output": "249.16787132207386 m/s\n The formula used is: math.sqrt((3 * r * t1 * 1000) / m)"
    },
    {
        "instruction": "A radioactive isotope has a half-life of 216 years. How long will it take the activity to reduce to 68.0 percent.\n",
        "input": "Time = Half Life/ln2 * ln(Initial Acitivity/Final Activity)",
        "output": "1.20e+02years\nTo calculate the time it takes for the activity of a radioactive isotope to reduce to a certain percentage, we can use the concept of half-life. The half-life (T) is the time it takes for the activity of a radioactive substance to reduce by half. To find the time required to reduce the activity to a certain percentage (p), we can use the formula: t = T * log(0.01) / log(p/100), where t is the time required, T is the half-life, and p is the desired percentage."
    },
    {
        "instruction": "A stone is thrown vertically upward and reaches a maximum height after 656842 s. With what initial velocity was it thrown up?",
        "input": "initial_velocity = acceleration * time",
        "output": "The stone was thrown upward with an initial velocity of 6437051.6 m/s."
    },
    {
        "instruction": "A body is dropped from the top of a building with an initial velocity of 4562 m/s under gravity, and it reaches the ground after 135 s. What is the height of the building?",
        "input": "initial velocity (u) = 4562 m/s, time (t) = 135 s",
        "output": "height (s) = initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)\u00b2\ns = 4562 * 135 + 0.5 * 9.8 * 135\u00b2\ns = 615870 + 89302.5\ns = 705172.5"
    },
    {
        "instruction": "A wire of material-1 of length 188 m and cross-sectional area 14 x 10^(-6) m^2 stretches by the same amount as a wire of material-2 of length 61 m and cross-sectional area 12 x 10^(-6) m^2 under a given load. What is the ratio of the Young\u2019s modulus of material-1 to that of material-2?",
        "input": "ratio = (l1 * A2) / (l2 * A1)",
        "output": "The ratio of the Young's modulus of material-1 to that of material-2 is approximately 2.64. To calculate the ratio, we use the formula:\n\nratio = (l1 * A2) / (l2 * A1)"
    },
    {
        "instruction": "Four point charges q1 = -6 x 10^(-6) C, q2 = 12 x 10^(-6) C, q3 = 20 x 10^(-6) C, q4 = -7 x 10^(-6) C, are located at corners of square ABCD of side 5 cm. What is the force on a charge of 6 x 10^(-6) C placed at the centre of the square?\n",
        "input": "Force (F) = k * |q1 - q3| * |q2 - q4| * q_c / (d^2)",
        "output": "To calculate the force on the charge placed at the center of the square, we use the formula for electric force between two point charges:\nForce (F) = k * |q1 - q3| * |q2 - q4| * q_c / (d^2)\nwhere k is Coulomb's constant (9 * 10^9 N\u00b7m\u00b2/C\u00b2), q1, q2, q3, q4 are the charges at the corners of the square (in Coulombs), q_c is the charge placed at the center of the square (in Coulombs), and d is the side length of the square (in meters).\nGiven q1 = -6 x 10^(-6) C, q2 = 12 x 10^(-6) C, q3 = 20 x 10^(-6) C, q4 = -7 x 10^(-6) C, d = 5 cm, and q_c = 6 x 10^(-6) C:\nForce (F) = 6.96e+02 N\n"
    },
    {
        "instruction": "A train runs along an unbanked circular track of radius 480 m at a speed of 186 m/s. The mass of the train is 24 kg. What is the angle of banking required to prevent wearing out of the rail?",
        "input": "((atan((v^2) / ((param + 400) * g))) * 180) / pi",
        "output": "82\nTo calculate the angle of banking, we use the formula ((atan((v^2) / ((param + 400) * g))) * 180) / pi, where v is the speed (186 m/s), g is the acceleration due to gravity (10 m/s^2), and param is the radius (480 m) of the circular track."
    },
    {
        "instruction": "A pump on the ground floor of a building can pump up water to fill a tank of volume 95 m3 in 5 min. If the tank is 86 m above the ground, and the efficiency of the pump is 79%, how much electric power is consumed by the pump?\n",
        "input": "(100000*v*h*9.8)/(t*e)",
        "output": "To find the electricity in the pump: (100000*v*h*9.8)/(t*e), this is the final answer 337831.22watts\n"
    },
    {
        "instruction": "A circular disc, of mass 11910 g, is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. If the period of torsional oscillations is 1350 ms, and the radius of the disc is 17 cm, determine the torsional spring constant of the wire.",
        "input": "Formula: alpha = (2\u03c0^2 * (m / 1000) * (r / 100)^2) / (t / 1000)^2, where alpha is the torsional spring constant, m is the mass of the disc in grams (11910 g), r is the radius of the disc in centimeters (17 cm), and t is the period of torsional oscillations in milliseconds (1350 ms).",
        "output": "Using this formula: Formula: alpha = (2\u03c0^2 * (m / 1000) * (r / 100)^2) / (t / 1000)^2, where alpha is the torsional spring constant, m is the mass of the disc in grams (11910 g), r is the radius of the disc in centimeters (17 cm), and t is the period of torsional oscillations in milliseconds (1350 ms)., this is the final answer derived: 3.73e+00 newton-m rad-1"
    },
    {
        "instruction": "A passenger arriving in a new town wishes to go from the station to a hotel located 141 km away on a straight road from the station. A dishonest cab man takes him along a circuitous path 211 km long and reaches the hotel in 20 min. What is (a) the average speed of the taxi, (b) the magnitude of average velocity? Are the two equal?",
        "input": "disp = 141 km, distance = 211 km, time = 20 min",
        "output": "The average speed of the taxi is 175.8 m/s. The magnitude of average velocity is 117.5 m/s. The two are not equal."
    },
    {
        "instruction": "In a process, 3246 J of heat is absorbed by a system and 3616 J of work is done on the system. What is the change in internal energy for the process ?\n",
        "input": "\u0394U = Q+W",
        "output": "from first law of thermodynamics, du = q + w => du = (+3246) + (+3616) => du = 6862joule\nQ is positive and W is positive as heat is absorbed by a system and work is done on system."
    },
    {
        "instruction": "If the position of the particle is given by r = (-10*t**2) i + (-t**3) j + (-3*t) k m, where t is in seconds, what is the acceleration of the particle (in vector notation)?",
        "input": "r = xi + yj + zk, v = dr/dt, a = dv/dt",
        "output": "The acceleration of the particle is (-20) i + (-6*t) j + (0) k m/s^2."
    },
    {
        "instruction": "A body of mass 9 kg is hanged from the roof with the help of a steel wire of length 2 m. Another body of mass 18 kg is hanged from the bottom of mass m1 with the help of a steel wire of length 1 m. If the radius of both wires is 105 x 10^(-4) m, what is the elongation of the steel wire?",
        "input": "elongation = (F * l) / (A * E)",
        "output": "elongation = (F * l) / (A * E)\nThe elongation of the wire is 7.6e-06 m."
    },
    {
        "instruction": "A convex lens produces a virtual image at a distance of 350 cm from it of a real object placed 178 cm in front of it. What is the magnification of the lens?",
        "input": "Formula: m = v / u",
        "output": "To calculate the magnification of the lens, we use the formula m = v / u, where m is the magnification, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for m. In this case, the magnification of the lens is 2.0., this is the final The magnification of the lens is 2.0."
    },
    {
        "instruction": "What is the gravitational potential at a point P at a distance of 183 m from the center of the uniform solid sphere of radius 207 m and mass 218 kg?",
        "input": "Gravitational Potential (V) = cal1(218, 183, 207) joule/kg",
        "output": "The gravitational potential at a point P at a distance of 183 m from the center of the uniform solid sphere of radius 207 m and mass 218 kg is given by the formula V = (-G * m * (3 * R^2 - r^2)) / (2 * R^3), where G is the gravitational constant, m is the mass, r is the distance, and R is the radius. Plugging in the values, we get V = -7.79e-11 joule/kg."
    },
    {
        "instruction": "A fighter plane flying horizontally at an altitude of 954 m with speed 289 ms-1 passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed 565 ms-1 to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit? (Take g = 10 ms-2)?",
        "input": "angle = asin(v1 / v2) * (180 / pi), minimum_altitude = (v2^2 * (1 - (v1 / v2)^2)) / (2 * g)",
        "output": "The angle from the vertical should be 30.8 degrees and the minimum altitude should be 11785.2 m."
    },
    {
        "instruction": "Two objects of masses 6 g and 15 g are moving along the same line and direction with velocities of 22 m/s and 20 m/s respectively. They collide and after the collision, the first object moves at a velocity of 1 m/s. Determine the velocity of the second object.",
        "input": "v2 = ((m1 * u1) + (m2 * u2) - (m1 * v1)) / m2",
        "output": "To find the velocity of the second object (v2), we use the formula:\n\nv2 = ((m1 * u1) + (m2 * u2) - (m1 * v1)) / m2\n\nSubstituting the given values, we have:\n\nv2 = ((6 * 22) + (15 * 20) - (6 * 1)) / 15\n\nSimplifying the expression gives us v2 = 28.4 m/s."
    },
    {
        "instruction": "A copper wire has a cross-sectional area of 9 m\u00b2, length of 30 m, and resistivity of 53 ohm-m. What is its resistance?",
        "input": "rho = 53 ohm-m, l = 30 m, A = 9 m\u00b2",
        "output": "The resistance of the wire is 176.7 ohm. It is calculated by dividing the product of resistivity and length (1590) by the area."
    },
    {
        "instruction": "A hollow sphere of mass 9243 kg has a radius of 49 m. What is the moment of inertia with respect to its symmetric axis?",
        "input": "Moment of Inertia = (Constant) * mass * radius^2",
        "output": "The moment of inertia with respect to its symmetric axis is approximately 14794962.0 kgm^2.\n\nMoment of Inertia = (Constant) * mass * radius^2\n\nConstant = 0.6666666666666666\nmass = 9243 kg\nradius = 49 m"
    },
    {
        "instruction": "A spring with a spring constant of 1719 Nm-1 is mounted on a horizontal table. A mass of 10 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 14 cm and released. Determine the maximum acceleration of the mass.",
        "input": "Formula: acceleration = (K * displacement) / mass",
        "output": "Using this formula: Formula: acceleration = (K * displacement) / mass, this is the final answer derived: 2.41e+01 m/s\u00b2"
    },
    {
        "instruction": "What is the side of a cube of volume 1805.223 cm3 (in m).\n",
        "input": "Volume = side^3",
        "output": "12176158\nCube of the side is it's volume."
    },
    {
        "instruction": "The coefficient of volume expansion of steel is 3.6e-05 K^-1. What is the change in its volume 59 m^3 for a rise in temperature from 72 degree C to 345 degree C?",
        "input": "Change in volume = d1 * a * (t2 - t1)",
        "output": "To find the change in volume, we use the following formula:\n\nChange in volume = d1 * a * (t2 - t1)\n\nSubstituting the given values into the formula, we find that the change in volume is approximately 0.58 m^3."
    },
    {
        "instruction": "An object is placed at 948 cm in front of a concave lens. Image is formed at a distance of 404 cm behind it. Find the focal length of the lens.",
        "input": "Formula: 1/f = 1/v - 1/u for concave lens.",
        "output": "This is the answer The focal length of the lens is 704 cm., formula used is : Formula: 1/f = 1/v - 1/u for concave lens."
    },
    {
        "instruction": "Suppose that the electric field amplitude of an electromagnetic wave is E0 = 1023 N/C and that its frequency is v = 594 MHz. Determine k?",
        "input": "v = 594 MHz",
        "output": "1.24e+01 rad/m\n\nThe wave number (k) can be determined by dividing the angular frequency by the speed of light."
    },
    {
        "instruction": "Find the ratio of time taken by the sound wave to travel a distance of 9 m in material-1 and material-2 (speed of sound in material-1 is 1857 m/s, in material-2 is 9854 m/s) ?\n",
        "input": "Speed = Distance/Time",
        "output": "5.3\nTo find the ratio of the time taken by the sound wave to travel a distance of 9 m in material-1 and material-2, we can use the equation: Ratio of time = time in material-1 / time in material-2. The time taken by the sound wave to travel a distance in material-1 can be calculated using the equation: time in material-1 = distance / speed in material-1. Similarly, the time taken by the sound wave to travel the same distance in material-2 can be calculated using: time in material-2 = distance / speed in material-2. Substituting the given values into the equations, we have: time in material-1 = 9 m / 1857 m/, time in material-2 = 9 m / 9854 m/s. Therefore, the ratio of the time taken by the sound wave to travel a distance of 9 m in material-1 and material-2 is: Ratio of time = (9 m / 1857 m/s) / (9 m / 9854 m/s)= 5.306408185245019"
    },
    {
        "instruction": "The peak voltage of an ac supply is 588641 mV. What is the rms voltage?",
        "input": "RMS Voltage = Peak Voltage / sqrt(2)",
        "output": "4.162e+02 volt"
    },
    {
        "instruction": "A 51 kg girl wearing high heel shoes. The heels are circular with a diameter 25527 micrometer. What is the pressure exerted by each of the heels on the horizontal floor?",
        "input": "51 * 4.9 / 0.0005117872215754501",
        "output": "The pressure exerted by each heel on the horizontal floor is 4.88e+05 newton. The pressure exerted by each heel on the horizontal floor is calculated using the formula P = (m * 4.9) / A, where m is the mass of the girl (51 kg) and A is the area of each heel (0.0005117872215754501 m^2)."
    },
    {
        "instruction": "A rope of negligible mass is wound round a solid sphere of mass 31 kg and radius 72 cm. What is the angular acceleration of the solid sphere if the rope is pulled with a force of 30 N? Assume that there is no slipping.",
        "input": "Acceleration = Force / (k * mass * radius)",
        "output": "Acceleration = 30 N / (0.4 * 31 kg * 72 cm)\n\nTo calculate the angular acceleration of the solid sphere, we use the following formula:\n\nAcceleration = Force / (k * mass * radius)\n\nSubstituting the values:\n\nForce = 30 N\nk = 0.4\nMass = 31 kg\nRadius = 72 cm\n\nWe find that the angular acceleration of the solid sphere is approximately 3.4 rad/s\u00b2."
    },
    {
        "instruction": "At t = 0, a wheel is rotating with an angular velocity of w rad/s at a constant angular acceleration of 26 rad/s\u00b2. It attains an angular velocity of 434 rad/s in t = 26 sec. What is the value of the initial angular velocity?",
        "input": "initial_angular_velocity = final_angular_velocity - (angular_acceleration * time)",
        "output": "To calculate the initial angular velocity, we use the following formula:\n\ninitial_angular_velocity = final_angular_velocity - (angular_acceleration * time)\n\nSubstituting the given values into the formula, we find that the initial angular velocity is approximately -242 rad/s."
    },
    {
        "instruction": "For an amplitude modulated wave, the maximum amplitude is found to be 17.44 V while the minimum amplitude is found to be 16.45 V. Determine the modulation index.\n",
        "input": "Modulation index = (a_max - a_min) / (a_max + a_min)",
        "output": "To determine the modulation index of an amplitude modulated wave, we use the formula modulation index = (a_max - a_min) / (a_max + a_min). Given the maximum amplitude (a_max) = 17.44 V and the minimum amplitude (a_min) = 16.45 V, the modulation index is equal to 0.03\n"
    },
    {
        "instruction": "If a point on the circumference of a wheel rotating with an angular velocity of 4 rad/s has a velocity of 966 m/s, what is the radius of the wheel?",
        "input": "radius = velocity / angular_velocity",
        "output": "To calculate the radius, we use the following formula:\n\nradius = velocity / angular_velocity\n\nSubstituting the given values into the formula, we find that the radius is approximately 241.5 m."
    },
    {
        "instruction": "A helicopter of mass 2342 kg rises with a vertical acceleration of 16 m/s^2. The crew and the passengers weigh 259 kg. Give the magnitude and direction of",
        "input": "force on the helicopter due to the surrounding air",
        "output": "67626 newton, vertically upwards\n\nThe force on the helicopter due to the surrounding air can be calculated based on the given mass (2342 kg), weight of crew and passengers (259 kg), and acceleration (16 m/s^2)."
    },
    {
        "instruction": "Two sitar strings A and B playing the note \u2018Ga\u2019 are slightly out of tune and produce beats of frequency 21 Hz. The tension in the string A is slightly increased and the beat frequency is found to be 2 Hz. If the original frequency of A is 703 Hz, what is the frequency of B?\n",
        "input": "Beat frequency = |f1+-f2|",
        "output": "724 hertz\nFrequency decreases with a decrease in the tension of a string.\nThis is because frequency is directly proportional to the square root of tension."
    },
    {
        "instruction": "A toroid has a core of inner radius 143 cm and outer radius 174 cm, around which 262 turns of a wire are wound. If the current in the wire is 23 A, what is the magnetic field inside the core of the solenoid.",
        "input": "Magnetic field = (mu * n * i) / l",
        "output": "To calculate the magnetic field inside the toroid, we use the following formula:\n\nMagnetic field = (mu * n * i) / l\n\nWhere,\n- n = Number of turns of the wire\n- i = Current in the wire\n- l = Length of the wire\n\nWe calculate the length of the wire using the formula:\n- Length of the wire = (r1 + r2) * pi\n\nSubstituting the given values and evaluating the formula, we find that the magnetic field inside the core of the toroid is approximately 7.60e-04 tesla."
    },
    {
        "instruction": "What is the density of water at a depth where pressure is 607900 Pa, given that its density at the surface is 1046 kg/m^3?",
        "input": "density = surface_density / (1 - depth * 45.8 * 10^(-8))",
        "output": "The density of water at a depth of 607900 Pa is approximately 1449.6 kg/m^3. To calculate the density, we use the formula:\n\ndensity = surface_density / (1 - depth * 45.8 * 10^(-8))"
    },
    {
        "instruction": "On a long horizontally moving belt, a child runs to and fro with a speed of 112 ms-1 (with respect to the belt) between his parents located 22 m apart on the moving belt. The belt moves with a speed of 69 ms-1. For an observer on a stationary platform outside, what is the time taken by the child to go from one parent to another parent?",
        "input": "time = distance / speed_relative",
        "output": "The time taken by the child to go from one parent to another parent is 0.5116279069767442 s."
    },
    {
        "instruction": "A convex lens produces 25 times magnified real image of height 60.02 cm of an object placed in front of it. What is the height of the object taken?",
        "input": "Formula: ho = hi / n",
        "output": "To find the height of the object taken, we use the formula ho = hi / n, where ho is the height of the object, hi is the height of the image, and n is the magnification factor. By substituting the given values into the formula, we can solve for ho. In this case, the height of the object taken is 2.4 cm., this is the final The height of the object taken is 2.4 cm."
    },
    {
        "instruction": "What is the pressure inside a drop of liquid of radius 19 mm at room temperature? Surface tension of liquid at that temperature (246 K) is 294 x 10^(-3) Nm^(-1). Also give the excess pressure inside the drop.",
        "input": "excess pressure = (2 * surface tension) / radius, total pressure = 1.01 * (10 ** 5) + excess pressure",
        "output": "The excess pressure inside the drop is 30.95 pascal. The total pressure inside the drop is 1.01e+05 pascal."
    },
    {
        "instruction": "An object is placed at 484 cm in front of a concave lens. Image is formed at a distance of 255 cm behind it. Find the focal length of the lens.",
        "input": "Formula: 1/f = 1/v - 1/u for concave lens.",
        "output": "This is the answer The focal length of the lens is 539 cm., formula used is : Formula: 1/f = 1/v - 1/u for concave lens."
    },
    {
        "instruction": "If a car has an initial velocity of 24 m/s and has a constant acceleration of 0 m/s\u00b2 for 31 s, then what is the final velocity of the car?",
        "input": "final_velocity = initial_velocity + (acceleration * time)",
        "output": "The final velocity of the car is 24 m/s."
    },
    {
        "instruction": "A long solenoid with 22 turns per cm has a small loop of area 28 cm\u00b2 placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 18 A to 22 A in 0.15 s, what is the induced emf in the loop while the current is changing?\n",
        "input": "EMF = (\u03bc\u2080 * A * n * I\u2082) / t",
        "output": "2.06e-04 volt\n\n\nThe induced electromotive force (EMF) can be calculated using the formula EMF = (\u03bc\u2080 * A * n * I\u2082) / t, where \u03bc\u2080 is the permeability of free space, A is the area of the loop, n is the number of turns per cm of the solenoid, I\u2082 is the change in current, and t is the time taken for the change."
    },
    {
        "instruction": "17 capacitors each of capacitance 176pF are connected in parallel. What is the charge on each capacitor if the combination is connected to a 336 V supply?\n",
        "input": "Q_capacitor = C_total * v\n",
        "output": "5.91e+04 pico-coulomb\n\nExplanation: Q_capacitor = 176 * 336 = 5.91e+04 pico-coulomb\n"
    },
    {
        "instruction": "To maintain a rotor at a uniform angular speed of 44 rad/s, an engine requires a power of 762 W. What is the torque transmitted by the engine?",
        "input": "Torque = Power / Angular Speed",
        "output": "Torque = 762 W / 44 rad/s\n\nTo calculate the torque transmitted by the engine, we use the following formula:\n\nTorque = Power / Angular Speed\n\nSubstituting the values:\n\nPower = 762 W\nAngular Speed = 44 rad/s\n\nWe find that the torque transmitted by the engine is 17.3 Nm."
    },
    {
        "instruction": "Light enters from a material-1 having refractive index 0.8 to material-2. If the speed of light in material-1 and material-2 is 292000000 m/s and 71000000 m/s respectively, what is the refractive index of material-2?",
        "input": "Speed of Light in a Material (v) = (n1 * c) / n2",
        "output": "The speed of light in a material can be calculated using the formula v = (n1 * c) / n2, where v is the speed of light in the material, n1 is the refractive index of material-1, c is the speed of light in vacuum, and n2 is the refractive index of material-2., this is the final 3.3"
    },
    {
        "instruction": "What is the gravitational potential at a point P at a distance of 213 m from the center of the spherical shell of radius 254 m and having 1.55e+02 C charge distributed uniformly on it.\n",
        "input": "To calculate the gravitational potential at a point outside a uniformly charged spherical shell, we use the formula:\n\nV = (k * Q) / R\n\nwhere V is the gravitational potential, k is the electrostatic constant (9 * 10^9 Nm^2/C^2), Q is the charge, and R is the distance from the center of the shell.",
        "output": "5.49e+09 joule/coulomb\n"
    },
    {
        "instruction": "A copper block of mass 3257 g is heated in a furnace to a temperature of 818 degree C and then placed on a large ice block. What is the maximum amount of ice that can melt? Specific heat of copper is 0.39 Jg-1\u00b0C-1. Heat of fusion of water = 335 Jg-1.",
        "input": "Maximum amount of ice melted = (mass of block * temperature change * specific heat) / heat of fusion of water",
        "output": "To calculate the maximum amount of ice melted, we use the following formula:\n\nMaximum amount of ice melted = (mass of block * temperature change * specific heat) / heat of fusion of water\n\nSubstituting the given values into the formula, we find that the maximum amount of ice that can melt is approximately 3101.6 g."
    },
    {
        "instruction": "In a Youngs double-slit experiment, the slits are seperated by 0.29 mm and the screen is placed 8.2 m away. The distance between the central bright fringe and the 6 bright fringe is measured to be 5 cm. Determine the wavelength of the ligth used for the experiment.\n",
        "input": "Distance between central bright fringe and bright fringe = (wavelength of light*distance from screen)/distance between slits",
        "output": "2.95e-07 m\nIn a Young's double-slit experiment, the wavelength of light can be determined using the formula: \u03bb = (d * sin(\u03b8)) / n, where \u03bb is the wavelength of light, d is the separation between the slits, \u03b8 is the angle of the fringe (in radians), and n is the order of the fringe."
    },
    {
        "instruction": "A wheel starting with an initial angular velocity of 84 rad/s is applied with a constant angular acceleration of 7 rad/s\u00b2. What is the time taken to reach an angular position of 953 rad?",
        "input": "time = (-(2 * initial_angular_velocity) + sqrt((4 * initial_angular_velocity^2) + (8 * angular_acceleration * angular_position))) / (2 * angular_acceleration)",
        "output": "To calculate the time, we use the following formula:\n\ntime = (-(2 * initial_angular_velocity) + sqrt((4 * initial_angular_velocity^2) + (8 * angular_acceleration * angular_position))) / (2 * angular_acceleration)\n\nSubstituting the given values into the formula, we find that the time is approximately 8.4 seconds."
    },
    {
        "instruction": "Two discs of moments of inertia 36 and 7 about their respective axes, and rotating with angular speed 79 rad/s and 98 rad/s are brought into contact face to face with their axes of rotation coincident. What is the angular speed of the two-disc system?",
        "input": "Angular Speed = ((i1 * w1) + (i2 * w2)) / (i1 + i2)\nLoss in Kinetic Energy = k1 + k2 - k\n\nk1 = 0.5 * i1 * w1^2\nk2 = 0.5 * i2 * w2^2\nk = 0.5 * (i1 + i2) * w^2",
        "output": "To calculate the angular speed and loss in kinetic energy, we use the following formulas:\n\nAngular Speed = ((i1 * w1) + (i2 * w2)) / (i1 + i2)\nLoss in Kinetic Energy = k1 + k2 - k\n\nWhere,\n- i1 = Moment of inertia of the first disc\n- i2 = Moment of inertia of the second disc\n- w1 = Angular speed of the first disc\n- w2 = Angular speed of the second disc\n\nSubstituting the given values into the formulas, we find that the angular speed of the two-disc system is approximately 82.1 rad/s rad/s"
    },
    {
        "instruction": "What is the focal length of a system of concave lens of focal length 18 cm, a concave lens of focal length 27 cm, and a convex lens of focal length 6 cm? Is the system a converging or a diverging lens? Ignore thickness of the lenses.",
        "input": "Formula: For a system of three lenses, the combined focal length (P) is given by P = (f1 * f2 * f3) / (f1 * f2 + f2 * f3 + f3 * f1), where f1, f2, and f3 are the focal lengths of the lenses.",
        "output": "This is the answer {answer}, formula used is : {formula}"
    },
    {
        "instruction": "Two heavy spheres each of mass 21 kg, 66 kg respectively are placed 135 m apart on a horizontal table. What is the gravitational potential at the mid point of the line joining the centres of the spheres?",
        "input": "Gravitational Potential (V) = -8.60e-11 joule/kg",
        "output": "The gravitational potential at the mid point of the line joining the centres of the spheres is given by the formula V = (-1 * G * m1 / R) - (G * m2 / R), where G is the gravitational constant, m1 and m2 are the masses of the spheres, and R is the distance between them. Plugging in the values, we get V = -8.60e-11 J/kg."
    },
    {
        "instruction": "Two bodies A, B of masses 39 kg and 173 kg respectively kept on a smooth, horizontal surface are tied to the ends of a tight string. A horizontal force F = 236 N is applied to B along the direction of the string. What is the acceleration and tension in the string?",
        "input": "",
        "output": "The acceleration is 1.1 m/s^2, and the tension is 43.4 N."
    },
    {
        "instruction": "A stone is thrown vertically upward and reaches a maximum height after 280012 s. With what initial velocity was it thrown up?",
        "input": "initial_velocity = acceleration * time",
        "output": "The stone was thrown upward with an initial velocity of 2744117.6 m/s."
    },
    {
        "instruction": "A long solenoid with 24 turns per cm has a small loop of area 12 cm\u00b2 placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 11 A to 21 A in 0.27 s, what is the induced emf in the loop while the current is changing?\n",
        "input": "EMF = (\u03bc\u2080 * A * n * I\u2082) / t",
        "output": "1.34e-04 volt\n\n\nThe induced electromotive force (EMF) can be calculated using the formula EMF = (\u03bc\u2080 * A * n * I\u2082) / t, where \u03bc\u2080 is the permeability of free space, A is the area of the loop, n is the number of turns per cm of the solenoid, I\u2082 is the change in current, and t is the time taken for the change."
    },
    {
        "instruction": "If a gas of 4 moles at 12 m3 is isothermally changed to volume 12 m3 at 10 K, then what is the work done.\n",
        "input": "Work Done = n*R*T*ln(V2/V1)",
        "output": "-0.0 joules\nTo calculate the work done during an isothermal expansion of a monoatomic gas, we can use the following equation: Work done = n * R * T * ln(V2/V1), where n is the number of moles of the gas, R is the ideal gas constant (approximately 8.314 J/(mol\u00b7K)), T is the temperature in Kelvin, V1 is the initial volume, and V2 is the final volume."
    },
    {
        "instruction": "A concave mirror produces 53 times diminished real image of an object placed at 9.94 cm in front of it. At what distance is the image formed from the mirror?",
        "input": "Formula: v = u / n",
        "output": "To find the distance at which the image is formed from the mirror, we use the formula v = u / n, where v is the distance of the image from the mirror, u is the distance of the object from the mirror, and n is the magnification factor. By substituting the given values into the formula, we can solve for v. In this case, the image is formed at a distance of 0.2 cm from the mirror., this is the final The image is formed at a distance of 0.2 cm from the mirror."
    },
    {
        "instruction": "A hollow cylinder of mass 9466 kg has a radius of 3 m. What is the moment of inertia with respect to its symmetric axis?",
        "input": "Moment of Inertia = (Constant) * mass * radius^2",
        "output": "The moment of inertia with respect to its symmetric axis is approximately 85194 kgm^2.\n\nMoment of Inertia = (Constant) * mass * radius^2\n\nConstant = 1\nmass = 9466 kg\nradius = 3 m"
    },
    {
        "instruction": "Given observations (tuples of I (in A) and V (in V)): (5, 85), (8, 136), (9, 153), (20, 341), (22, 374), (25, 425); Determine whether the given conductor is an ohmic conductor or not.\n",
        "input": "",
        "output": "No, it is not an ohmic conductor.\n"
    },
    {
        "instruction": "A rigid bar of mass 2 kg is supported symmetrically by three wires each 17 m long. Those at each end are of material-1 and the middle one is of material-2. Find ratios of their diameters all have the same tension (Young's modulus of material-1 is 20 x 10^9 Nm-2, material-2 is 134 x 10^9 Nm-2).",
        "input": "diameter_ratio = sqrt(Y2 / Y1)",
        "output": "The ratio of their diameters is 2.59."
    },
    {
        "instruction": "If a diatomic gas of 6 moles at 120 atm and volume 72 lit is isothermally changed to volume 195 lit, then what will be the pressure.\n",
        "input": "P1*V1 = P2*V2",
        "output": "44.3atm\nTo determine the final pressure of a diatomic gas after an isothermal expansion, we can use Boyle's Law, which states that for an ideal gas at constant temperature: P1 * V1 = P2 * V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume."
    },
    {
        "instruction": "A copper block of mass 3134 g is heated in a furnace to a temperature of 742 degree C and then placed on a large ice block. What is the maximum amount of ice that can melt? Specific heat of copper is 0.39 Jg-1\u00b0C-1. Heat of fusion of water = 335 Jg-1.",
        "input": "Maximum amount of ice melted = (mass of block * temperature change * specific heat) / heat of fusion of water",
        "output": "To calculate the maximum amount of ice melted, we use the following formula:\n\nMaximum amount of ice melted = (mass of block * temperature change * specific heat) / heat of fusion of water\n\nSubstituting the given values into the formula, we find that the maximum amount of ice that can melt is approximately 2707.2 g."
    },
    {
        "instruction": "A concave lens produces 95 times diminished real image of an object placed at 273 cm in front of it. At what distance is the image formed from the lens?",
        "input": "Formula: v = u / n",
        "output": "To find the distance at which the image is formed, we use the formula v = u / n, where v is the distance of the image from the lens, u is the distance of the object from the lens, and n is the magnification factor. By substituting the given values into the formula, we can solve for v. In this case, the image is formed at a distance of 2.9 cm., this is the final The image is formed at a distance of 2.9 cm."
    },
    {
        "instruction": "Two absolute scales A and B have triple points of water defined to be -114 A and -47 B. What is the relation between TA and TB?",
        "input": "Relation between TA and TB = TA / TB",
        "output": "To find the relation between TA and TB, we divide the temperature on scale A (TA) by the temperature on scale B (TB). Therefore, the relation is given by:\n\nRelation between TA and TB = TA / TB\n\nSubstituting the given values, we find that the relation is approximately 2.43."
    },
    {
        "instruction": "What is the gravitational field at a point P on the surface of the spherical shell of radius 269 m and mass 79 kg?",
        "input": "Gravitational Field (g) = cal3(79, 269) N/kg",
        "output": "The gravitational field at a point P on the surface of the spherical shell of radius 269 m and mass 79 kg is given by the formula g = (-G * m) / (r^2), where G is the gravitational constant, m is the mass, and r is the distance. Plugging in the values, we get g = -7.28e-14 N/kg."
    },
    {
        "instruction": "The mass of a particle is 3.7900000000000006e-29 kg. If its velocity is 5935 m/s, calculate its wavelength.\n",
        "input": "Wavelength = h/mass*velocity",
        "output": "0.1m\nThe momentum (p) of a particle is given by the product of its mass (m) and velocity (v), according to the formula P=M*VThe wavelength (\u03bb) of a particle can be calculated using the de Broglie wavelength equation, which relates the wavelength of a particle to its momentum."
    },
    {
        "instruction": "A 100 kW drilling machine is used to drill a bore in a small aluminium block of mass 11 kg. How much is the rise in temperature of the block in 1 minutes, assuming 54 percent of power is used up in heating the machine itself or lost to the surroundings? Specific heat of aluminium = 0.91 J g-1 K-1.",
        "input": "Rise in temperature = (p * P * t) / (m * s)",
        "output": "To calculate the rise in temperature, we use the following formula:\n\nRise in temperature = (p * P * t) / (m * s)\n\nSubstituting the given values into the formula, we find that the rise in temperature is approximately 539.5 degrees Celsius."
    },
    {
        "instruction": "A cyclist is riding with a speed of 138 m/s. As he approaches a circular turn on the road of radius 162 m, he applies brakes and reduces his speed at a constant rate of 77 m/s\u00b2 every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn?",
        "input": "a = v\u00b2/r, a = \u221a(a\u00b2 + b\u00b2), b = v\u00b2/r",
        "output": "magnitude is 140.5 ms-2, 57 degrees from the -ve direction of velocity, a = 117.6 ms-2, b = 77 ms-2\n {explanation}"
    },
    {
        "instruction": "The equilibrium constant for a reaction is 777. Calculate the value of \u0394G^o, given R = 8.3 J/Kmol and T = 295.5.\n",
        "input": "\u0394G^o = -2.303RTlogK or -RTlnK",
        "output": "-37592.9\nTo calculate the standard Gibbs free energy change (\u0394G^o) for a reaction given the equilibrium constant (K), gas constant (R), and temperature (T), we can use the following equation: \u0394G^o = -R * T * ln(K) where ln represents the natural logarithm."
    },
    {
        "instruction": "To maintain a rotor at a uniform angular speed of 213 rad/s, an engine requires a power of 531 W. What is the torque transmitted by the engine?",
        "input": "Torque = Power / Angular Speed",
        "output": "Torque = 531 W / 213 rad/s\n\nTo calculate the torque transmitted by the engine, we use the following formula:\n\nTorque = Power / Angular Speed\n\nSubstituting the values:\n\nPower = 531 W\nAngular Speed = 213 rad/s\n\nWe find that the torque transmitted by the engine is 2.5 Nm."
    },
    {
        "instruction": "A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 28 Hz. The mass of the wire is 0.176 kg and its linear mass density is 0.056 kg m-3. What is the speed of a transverse wave on the string?\n",
        "input": "Speed^2 = Tension*length/mass",
        "output": "1.76e+02 ms-1\nTo find the length of the wire, we can use the formula for the fundamental frequency of a vibrating wire:\nf = (1/2L) * sqrt(T / \u03bc)\n\nWhere f is the frequency, L is the length of the wire, T is the tension in the wire, and \u03bc is the linear mass density.\n\nWe can rearrange the formula to solve for L:\n\nL = (1/2) * sqrt(T / (f^2 * \u03bc))\n\nGiven that the frequency f is \"+str(f)+\" Hz, the mass m is \"+str(m)+\" kg, and the linear mass density \u03bc is \"+str(mu)+\" kg/m\u00b3, we need to determine the tension T in the wire.\n\nThe tension T can be calculated using the formula:\n\nT = \u03bc * g * L\n\nWhere g is the acceleration due to gravity.\n\nSubstituting the known values into the formula, we can calculate the tension T.\n\nOnce we have the tension T, we can substitute it and the other known values into the formula for L to find the length of the wire in its fundamental mode.\n\nL = (1/2) * sqrt(T / (f^2 * \u03bc))\n\nCalculating this expression will give us the length of the wire."
    },
    {
        "instruction": "A concave mirror produces 24 times magnified virtual image of an object placed at 18.26 cm in front of it. At what distance is the image formed from the mirror?",
        "input": "Formula: v = u / n",
        "output": "To find the distance at which the image is formed from the mirror, we use the formula v = u / n, where v is the distance of the image from the mirror, u is the distance of the object from the mirror, and n is the magnification factor. By substituting the given values into the formula, we can solve for v. In this case, the image is formed at a distance of 0.8 cm from the mirror., this is the final The image is formed at a distance of 0.8 cm from the mirror."
    },
    {
        "instruction": "A uniformly charged conducting sphere of 728 cm diameter has a surface charge density of 1479 micro-C/m\u00b2, then find the electric flux leaving the sphere?\n",
        "input": "Electric flux = Surface charge density * Surface area * (1 / (4 * pi * epsilon_0))",
        "output": "To calculate the electric flux leaving the sphere, we use the formula:\nElectric flux = Surface charge density * Surface area * (1 / (4 * pi * epsilon_0))\nGiven surface charge density = 1479 micro-C/m\u00b2, diameter = 728 cm,\nElectric flux = 2.78e+10 N\u00b7m\u00b2/C\n"
    },
    {
        "instruction": "If a wheel of radius 419 m has an angular acceleration of 214 rad/s\u00b2, what is the acceleration of a point at the circumference of the wheel?",
        "input": "acceleration_at_circumference = angular_acceleration * radius",
        "output": "To calculate the acceleration at the circumference, we use the following formula:\n\nacceleration_at_circumference = angular_acceleration * radius\n\nSubstituting the given values into the formula, we find that the acceleration at the circumference is approximately 89666 m/s\u00b2."
    },
    {
        "instruction": "Four point charges q1 = -5 x 10^(-6) C, q2 = 20 x 10^(-6) C, q3 = -6 x 10^(-6) C, q4 = -8 x 10^(-6) C, are located at corners of square ABCD of side 13 cm. What is the force on a charge of 17 x 10^(-6) C placed at the centre of the square?\n",
        "input": "Force (F) = k * |q1 - q3| * |q2 - q4| * q_c / (d^2)",
        "output": "To calculate the force on the charge placed at the center of the square, we use the formula for electric force between two point charges:\nForce (F) = k * |q1 - q3| * |q2 - q4| * q_c / (d^2)\nwhere k is Coulomb's constant (9 * 10^9 N\u00b7m\u00b2/C\u00b2), q1, q2, q3, q4 are the charges at the corners of the square (in Coulombs), q_c is the charge placed at the center of the square (in Coulombs), and d is the side length of the square (in meters).\nGiven q1 = -5 x 10^(-6) C, q2 = 20 x 10^(-6) C, q3 = -6 x 10^(-6) C, q4 = -8 x 10^(-6) C, d = 13 cm, and q_c = 17 x 10^(-6) C:\nForce (F) = 2.54e+02 N\n"
    },
    {
        "instruction": "A solid cylinder of mass 3512 kg has a radius of 88 m and length of 61 m. What is the moment of inertia with respect to its diameter?",
        "input": "Moment of Inertia = (Constant1) * mass * length^2 + (Constant2) * mass * radius^2",
        "output": "The moment of inertia with respect to its end is approximately 1089012.7 kgm^2.\n\nMoment of Inertia = (Constant1) * mass * length^2 + (Constant2) * mass * radius^2\n\nConstant1 = 0.08333333333333333\nConstant2 = 0.5\nmass = 3512 kg\nlength = 61 m\nradius = 88 m"
    },
    {
        "instruction": "A concave mirror produces 79 times magnified virtual image of an object placed at 23.97 cm in front of it. At what distance is the image formed from the mirror?",
        "input": "Formula: v = u / n",
        "output": "To find the distance at which the image is formed from the mirror, we use the formula v = u / n, where v is the distance of the image from the mirror, u is the distance of the object from the mirror, and n is the magnification factor. By substituting the given values into the formula, we can solve for v. In this case, the image is formed at a distance of 0.3 cm from the mirror., this is the final The image is formed at a distance of 0.3 cm from the mirror."
    },
    {
        "instruction": "A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 138 Hz. The mass of the wire is 0.037 kg and its linear mass density is 0.045 kg m-3. What is the tension in the string?\n",
        "input": "Speed^2 = Tension*length/mass",
        "output": "2.32e+03 newton\nTo find the length of the wire, we can use the formula for the fundamental frequency of a vibrating wire:\nf = (1/2L) * sqrt(T / \u03bc)\n\nWhere f is the frequency, L is the length of the wire, T is the tension in the wire, and \u03bc is the linear mass density.\n\nWe can rearrange the formula to solve for L:\n\nL = (1/2) * sqrt(T / (f^2 * \u03bc))\n\nGiven that the frequency f is \"+str(f)+\" Hz, the mass m is \"+str(m)+\" kg, and the linear mass density \u03bc is \"+str(mu)+\" kg/m\u00b3, we need to determine the tension T in the wire.\n\nThe tension T can be calculated using the formula:\n\nT = \u03bc * g * L\n\nWhere g is the acceleration due to gravity.\n\nSubstituting the known values into the formula, we can calculate the tension T.\n\nOnce we have the tension T, we can substitute it and the other known values into the formula for L to find the length of the wire in its fundamental mode.\n\nL = (1/2) * sqrt(T / (f^2 * \u03bc))\n\nCalculating this expression will give us the length of the wire."
    },
    {
        "instruction": "15 identical hollow cylindrical columns of mild steel support a big structure of mass 18260 kg. The inner and outer radii of each column are 35 cm and 73 cm respectively. Calculate the compressional strain of each column.",
        "input": "strain = F / (A * Y)",
        "output": "The compressional strain of each column is 4.6e-08."
    },
    {
        "instruction": "Two long and parallel straight wires A and B carrying currents of 35 A and 46 A in the same direction are separated by a distance 93 cm. Estimate the force and its nature on the 17 cm section of wire A.",
        "input": "Force = (mu * i1 * i2 * l) / (2 * pi * r)",
        "output": "To calculate the force and its nature, we use the following formula:\n\nForce = (mu * i1 * i2 * l) / (2 * pi * r)\n\nSubstituting the given values:\n- mu = 4 * pi * 10^(-7) TmA^-1\n- i1 = 35 A\n- i2 = 46 A\n- r = 93 cm\n- l = 17 cm\n\nAfter evaluating the formula, we find that the force on the 17 cm section of wire is approximately 5.89e-05 newtons and attractive."
    },
    {
        "instruction": "During blood transfusion, the needle is inserted in a vein where the gauge pressure is 4794 Pa. If the blood container is placed at 407 mm above the Earth's level so that blood may just enter the vein, is it safe for the patient?",
        "input": "(4794 / (1060 * 9.8)) * 1000",
        "output": "No, the patient is not safe."
    },
    {
        "instruction": "In a meter bridge, the balance point is found to be at 269 mm from end A, when the resistor Y is of 1414 ohm. Determine the resistance of X.",
        "input": "Resistance of X = ((1000 - balance_point) / balance_point) * R1",
        "output": "3842.5 ohm\n\nExplanation: The resistance of X in the meter bridge can be calculated using the formula: Resistance of X = ((1000 - balance_point) / balance_point) * R1."
    },
    {
        "instruction": "A circular coil of radius 38 cm and 4 turns is rotated about its vertical diameter with an angular speed of 70 rad/s in a uniform horizontal magnetic field of magnitude 2.2 T. Obtain the maximum and average emf induced in the coil. If a coil forms a closed loop of resistance 2 ohm, what is the maximum current in the coil and average power loss due to joule heating?\n",
        "input": "EMF = n * w * b * A, I = EMF / R, P = (EMF * I) / 2",
        "output": "maximum emf: 2.79e+02 volt, average emf: 0 volts, maximum current: 1.40e+02 amp, average power loss: 1.95e+04 joule\n\n\nThe maximum emf induced in the coil can be calculated using the formula EMF = n * w * b * A, where n is the number of turns, w is the angular speed, b is the magnetic field magnitude, and A is the area of the coil.\nThe maximum current in the coil can be calculated using the formula I = EMF / R, where R is the resistance of the coil.\nThe average power loss due to joule heating can be calculated using the formula P = (EMF * I) / 2."
    },
    {
        "instruction": "A passenger arriving in a new town wishes to go from the station to a hotel located 206 km away on a straight road from the station. A dishonest cab man takes him along a circuitous path 214 km long and reaches the hotel in 27 min. What is (a) the average speed of the taxi, (b) the magnitude of average velocity? Are the two equal?",
        "input": "disp = 206 km, distance = 214 km, time = 27 min",
        "output": "The average speed of the taxi is 132.1 m/s. The magnitude of average velocity is 127.2 m/s. The two are not equal."
    },
    {
        "instruction": "A solid sphere rolls down two different inclined planes of heights 13 cm and 10 cm and with angles of inclination of 79 and 71, on which it reaches the bottom with more speed?",
        "input": "speed = height / (k + 1)",
        "output": "To compare the speeds, we use the following formula:\n\nspeed = height / (k + 1)\n\nSubstituting the given values into the formula, we find that:\n\nThe first plane has more speed."
    },
    {
        "instruction": "A steel rod 1108 cm long is hinged at its middle. The fundamental frequency of longitudinal vibrations of the rod is given to be 1846 Hz. What is the speed of sound in steel?\n",
        "input": "speed of sound in steel = frequency*wavelength",
        "output": "4.1e+04 ms-1\nThe distance between two successive nodes is wavelength/2."
    },
    {
        "instruction": "Two discs of moments of inertia 41 and 100 about their respective axes, and rotating with angular speed 70 rad/s and 82 rad/s are brought into contact face to face with their axes of rotation coincident. What is the loss in kinetic energy of the two-disc system?",
        "input": "Angular Speed = ((i1 * w1) + (i2 * w2)) / (i1 + i2)\nLoss in Kinetic Energy = k1 + k2 - k\n\nk1 = 0.5 * i1 * w1^2\nk2 = 0.5 * i2 * w2^2\nk = 0.5 * (i1 + i2) * w^2",
        "output": "To calculate the angular speed and loss in kinetic energy, we use the following formulas:\n\nAngular Speed = ((i1 * w1) + (i2 * w2)) / (i1 + i2)\nLoss in Kinetic Energy = k1 + k2 - k\n\nWhere,\n- i1 = Moment of inertia of the first disc\n- i2 = Moment of inertia of the second disc\n- w1 = Angular speed of the first disc\n- w2 = Angular speed of the second disc\n\nSubstituting the given values into the formulas, we find that the loss in kinetic energy is approximately 2093.6 joules joules."
    },
    {
        "instruction": "In a process, 1293 J of heat is absorbed by a system and 8567 J of work is done by the system. What is the change in internal energy for the process ?\n",
        "input": "\u0394U = Q+W",
        "output": "from first law of thermodynamics, du = q + w => du = (+1293) + (-8567) => du = -7274joule\nQ is positive and W is negative as heat is absorbed by a system and work is done by system."
    },
    {
        "instruction": "Calculate the enthalpy change on freezing of 11 mol of water at 0.3 celcius to ice at -52.2 celcius.\n",
        "input": "(\u0394H)=(\u0394H1)+(\u0394H2)",
        "output": "45447.6\nTotal enthalpy change involved in the transformation is the sum of the following changes and can be represented using the Hess Law."
    },
    {
        "instruction": "What is the gravitational potential at a point P at a distance of 378 m from a mass of 290 kg?",
        "input": "Gravitational Potential (V) = cal3(290, 378) joule/kg",
        "output": "The gravitational potential at a point P at a distance of 378 m from a mass of 290 kg is given by the formula V = (-G * m) / r, where G is the gravitational constant, m is the mass, and r is the distance. Plugging in the values, we get V = -5.12e-11 joule/kg."
    },
    {
        "instruction": "What is the gravitational force between two masses 95000 kg and 15000 kg seperated bt a distance 44 m.\n",
        "input": "f = (g x m1 x m2)/d^2",
        "output": "the gravitational between two bodies of masses m1 and m2 seperated by a distance d is given by, f = (g x m1 x m2)/d^2 = (6.67 x 10^-11 x 95000 x 10^-3 x 15000 x 10^-3)/44^2 = 4.91e-05 newton\n"
    },
    {
        "instruction": "A meter stick is balanced on a knife edge at its center. When two coins, each of mass 24 g and 22 g respectively, are put at the 20 mark and 96 mark respectively, the stick is found to be balanced at 1 cm. What is the mass of the meter stick?",
        "input": "Mass = (Right Side - Left Side) / Distance",
        "output": "The mass of the meter stick is approximately -52.0 g.\nLeft Side = m1 * (t3 - t1) = 24 * (1 - 20)\nRight Side = m2 * (t2 - t3) = 22 * (96 - 1)"
    },
    {
        "instruction": "An air bubble of volume 57 cm3 rises from the bottom of a lake 125 m deep at a temperature of 24 degree C. To what volume does it grow when it reaches the surface, which is at a temperature of 34 degree C.",
        "input": "(p1 * v * t2) / (t1 * p2)",
        "output": "780.7 cm3\np1 = initial pressure\np2 = final pressure\nV = volume\nt1 = initial temperature\nt2 = final temperature\nR = gas constant\nn = (1325000.0 * 57 * 10^5) / (8.314 * 297) - (100000 * 57 * 10^5) / (8.314 * 307)\nn = 3058611129.3 - 223319403.9\nn = 2835291725.4\nV = n * R * t2 / p2 = 723.7 cm3"
    },
    {
        "instruction": "A concave mirror produces 54 times magnified virtual image of a 13.16 cm object placed in front of it. What is the height of the image formed by the mirror?",
        "input": "Formula: hi = n * ho",
        "output": "To find the height of the image formed by the mirror, we use the formula hi = n * ho, where hi is the height of the image, n is the magnification factor, and ho is the height of the object. By substituting the given values into the formula, we can solve for hi. In this case, the height of the image formed by the mirror is 710.6 cm., this is the final The height of the image formed by the mirror is 710.6 cm."
    },
    {
        "instruction": "A stone of mass 267 g dropped from the top of a tower of height 50 m high splashes into the water of a pond near the base of the tower. When is the splash heard at the top given.\n",
        "input": "Height = Initial Speed + 1/2*g*time^2, Total time = t1+t2",
        "output": "3.34 s\nUse the equation of motion: Height = Initial Speed + 1/2*g*time^2, to calculate the time of splash heard."
    },
    {
        "instruction": "A 20 watt bulb emits monochromatic yellow light of wavelength 754618 pm. Calculate the rate of emission of quanta per second.\n",
        "input": "Rate of emission per quanta = Power*wavelength/h*c",
        "output": "7.62e+19per second\nTo calculate the rate of emission of quanta per second, we need to determine the number of photons emitted per second by the light bulb.The energy of each photon can be calculated using the formula: Energy of each photon = h * c / \u03bb, where h is the Planck constant (approximately 6.626 x 10^-34 J\u00b7s), c is the speed of light (approximately 3 x 10^8 m/s), and \u03bb is the wavelength of light in meters.Now, we can calculate the rate of emission of quanta per second using the formula: Rate of emission = Power / Energy of each photon, where Power is the power of the light bulb in watts."
    },
    {
        "instruction": "A passenger arriving in a new town wishes to go from the station to a hotel located 34 km away on a straight road from the station. A dishonest cab man takes him along a circuitous path 60 km long and reaches the hotel in 1 min. What is (a) the average speed of the taxi, (b) the magnitude of average velocity? Are the two equal?",
        "input": "disp = 34 km, distance = 60 km, time = 1 min",
        "output": "The average speed of the taxi is 1000.0 m/s. The magnitude of average velocity is 566.7 m/s. The two are not equal."
    },
    {
        "instruction": "In a uniform electric field of 2930 N/C, what is the flux through a square of 40 cm, whose plane is at 7 degrees angle with the x-axis?\n",
        "input": "Flux = Electric field * Area * cos(theta)",
        "output": "To calculate the flux through the square, we use the formula:\nFlux = Electric field * Area * cos(theta)\nGiven electric field = 2930 N/C, area = 1600 cm\u00b2, theta = 7 degrees,\nFlux = 4.65e+02 N\u00b7m\u00b2/C\n"
    },
    {
        "instruction": "A long straight wire in the horizontal plane carries a current of of 213 A in south to north direction. What is the magnitude and direction of the magnetic field B at a point 1080 cm east of the wire.\n",
        "input": "B = (mu * i) / (2 * pi * r)",
        "output": "To calculate the magnitude and direction of the magnetic field B, we use the following formula:\n\nB = (mu * i) / (2 * pi * r)\n\nWhere,\n- B = Magnetic field\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- i = Current flowing through the wire\n- r = Distance from the wire\n\nSubstituting the given values into the formula, we find that the magnitude and direction of the magnetic field B is approximately 3.9e-06 tesla vertically downwards\n."
    },
    {
        "instruction": "If an artificial satellite is moving in a circular orbit of radius 1449 m, then calculate its speed if it takes 262 s to complete a rotation?",
        "input": "r = 1449 m, t = 262 s",
        "output": "The speed of the satellite is 34.7 m/s."
    },
    {
        "instruction": "Two objects collide and their masses are unknown. Their initial velocities are 17 m/s and 27 m/s respectively. After the collision, the first object moves at a velocity of 7 m/s and the second object moves at a velocity of 21 m/s. Determine the mass of the first object.",
        "input": "m1 = (m2 * (v2 - u2)) / (u1 - v1)",
        "output": "To find the mass of the first object (m1), we use the formula:\n\nm1 = (m2 * (v2 - u2)) / (u1 - v1)\n\nSubstituting the given values, we have:\n\nm1 = (8 * (21 - 27)) / (17 - 7)\n\nSimplifying the expression gives us m1 = -4.8 g."
    },
    {
        "instruction": "An object of mass 1958 g stands on a weighing machine in a lift, which is moving upwards with a uniform acceleration of 223 cm/s^2.",
        "input": "Scale Reading = m * (10 + (acc / 100))",
        "output": "23.9\nTo calculate the scale reading, we use the formula Scale Reading = mass * (10 + (acceleration / 100)), where the mass is 1958 g and the acceleration is 223 cm/s^2."
    },
    {
        "instruction": "A bullet of mass 330 g and speed 1143 m/s is fired into a door and gets embedded at the center of the door. The door is 32 m wide and weighs 44 kg. It is hinged at one end and rotates about a vertical axis. Find the angular speed of the door just after the bullet embeds into it.",
        "input": "Angular Speed = (m1 * v1 * l) / (1000 * 2 * I)",
        "output": "To calculate the angular speed of the door, we use the following formula:\n\nAngular Speed = (m1 * v1 * l) / (1000 * 2 * I)\n\nWhere,\n- m1 = Mass of the bullet\n- v1 = Speed of the bullet\n- l = Width of the door\n- I = Moment of inertia of the door\n\nThe moment of inertia of the door can be calculated as I = (m2 * l\u00b2) / 3, where m2 is the mass of the door.\n\nSubstituting the given values into the formula, we find that the angular speed of the door is approximately 0.4 rad/s."
    },
    {
        "instruction": "To maintain a rotor at a uniform angular speed of 54 rad/s, an engine requires a power of 297 W. What is the torque transmitted by the engine?",
        "input": "Torque = Power / Angular Speed",
        "output": "Torque = 297 W / 54 rad/s\n\nTo calculate the torque transmitted by the engine, we use the following formula:\n\nTorque = Power / Angular Speed\n\nSubstituting the values:\n\nPower = 297 W\nAngular Speed = 54 rad/s\n\nWe find that the torque transmitted by the engine is 5.5 Nm."
    },
    {
        "instruction": "A liquid has an angle of contact equal to 68 degrees with soda-lime glass. A narrow tube of radius 10 mm made of this glass is dipped in a trough containing liquid. By what amount does the liquid dip down in the tube relative to the liquid surface outside? Surface tension of liquid is 0.62 Nm-2. Density of liquid = 17 x 10^3 kgm-3.",
        "input": "(2 * st * cos(angle * pi / 180)) / (r * density * 9.8)",
        "output": "The liquid in the narrow tube dips down by an amount given by (2 * st * cos(angle * pi / 180)) / (r * density * 9.8). Substituting the given values, we have (2 * 0.62 * cos(68 * 3.141592653589793 / 180)) / (10 * 17 * 10^3 * 9.8) = 2.79e-04 m."
    },
    {
        "instruction": "A circular coil of 50 turns and radius 18 cm carrying a current of 44 A rests with its plane normal to an external field of magnitude 0.05 T. The coil is free to turn about an axis in its plane perpendicular to the field direction. When the coil is turned slightly and released, it oscillates about its stable equilibrium with a frequency of 11 sec-1. What is the moment of inertia of the coil about its axis of rotation?",
        "input": "(m * b) / (4 * pi^2 * v^2)",
        "output": "The moment of inertia of the coil about its axis of rotation can be calculated using the formula (m * b) / (4 * pi^2 * v^2), where 'm' is the mass of the coil given by n * i * pi * r^2, 'b' is the magnitude of the external magnetic field, 'v' is the frequency of oscillation. Substituting the given values, we have (223.93272434788045 * 0.05) / (4 * 3.141592653589793^2 * 11^2) = 0.002343918252807913 kgm^2."
    },
    {
        "instruction": "Two copper spheres A, B are separated by a distance 29 cm. The force of repulsion if the charge on A is 4e-06 C, and the charge on B is -1.4999999999999999e-05 C is F1. The force of repulsion if the charge on A becomes 2 times, the charge on B becomes 5 times, and the distance between them becomes 4 times is F2. Find F1/F2?\n",
        "input": "F1/F2 = (d2^2) / (r1 * r2)",
        "output": "16/10"
    },
    {
        "instruction": "Two towers on top of two hills are 78 km apart. The line joining them passes 69 m above a hill halfway between the towers. What is the longest wavelength of radio waves, which can be sent between the two towers without appreciable diffraction effects.\n",
        "input": "Fresnel Distance*Aperture = Wavelength of light^2",
        "output": "6.10e-02 m\nTo determine the longest wavelength of radio waves that can be sent between the two towers without appreciable diffraction effects, we can use the Fresnel diffraction criterion. The Fresnel diffraction criterion states that when the distance (d) between the two towers is much larger than the square of the wavelength (\u03bb), diffraction effects can be neglected.In this case, we want to find the maximum wavelength, so we can rearrange the formula to solve for \u03bb: \u03bb \u2248 sqrt(d * l)"
    },
    {
        "instruction": "The peak voltage of an ac supply is 6789 mV. What is the rms voltage?",
        "input": "RMS Voltage = Peak Voltage / sqrt(2)",
        "output": "4.801e+00 volt"
    },
    {
        "instruction": "If a car has an initial velocity of 152 m/s and has a constant acceleration of 17 m/s\u00b2, then what is the time taken by the car to attain a velocity of 528 m/s?",
        "input": "time = (final_velocity - initial_velocity) / acceleration",
        "output": "The time taken by the car to attain a velocity of 528 m/s is 22.1 s."
    },
    {
        "instruction": "Estimate the fraction of molecular volume to the actual volume occupied by a gas at STP. Take the diameter of the gas molecule to be 75.6 A.",
        "input": "(4 * pi * d * d * d * 1000 * n) / (3 * 8 * 22.4)",
        "output": "6.083154595713601e+30 \n (4 * pi * d * d * d * 1000 * n) / (3 * 8 * 22.4)"
    },
    {
        "instruction": "A concave lens produces 78 times diminished real image of height 34.84 cm of an object placed in front of it. What is the height of the object?",
        "input": "Formula: ho = n * hi",
        "output": "To find the height of the object, we use the formula ho = n * hi, where ho is the height of the object, hi is the height of the image, and n is the magnification factor. By substituting the given values into the formula, we can solve for ho. In this case, the height of the object is 2717.5 cm., this is the final The height of the object is 2717.5 cm."
    },
    {
        "instruction": "A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 135 Hz. The mass of the wire is 0.088 kg and its linear mass density is 0.008 kg m-3. What is the tension in the string?\n",
        "input": "Speed^2 = Tension*length/mass",
        "output": "7.06e+04 newton\nTo find the length of the wire, we can use the formula for the fundamental frequency of a vibrating wire:\nf = (1/2L) * sqrt(T / \u03bc)\n\nWhere f is the frequency, L is the length of the wire, T is the tension in the wire, and \u03bc is the linear mass density.\n\nWe can rearrange the formula to solve for L:\n\nL = (1/2) * sqrt(T / (f^2 * \u03bc))\n\nGiven that the frequency f is \"+str(f)+\" Hz, the mass m is \"+str(m)+\" kg, and the linear mass density \u03bc is \"+str(mu)+\" kg/m\u00b3, we need to determine the tension T in the wire.\n\nThe tension T can be calculated using the formula:\n\nT = \u03bc * g * L\n\nWhere g is the acceleration due to gravity.\n\nSubstituting the known values into the formula, we can calculate the tension T.\n\nOnce we have the tension T, we can substitute it and the other known values into the formula for L to find the length of the wire in its fundamental mode.\n\nL = (1/2) * sqrt(T / (f^2 * \u03bc))\n\nCalculating this expression will give us the length of the wire."
    },
    {
        "instruction": "A 3m long tube open at one end, with a movable piston at the other end, shows resonance with a fixed frequency source (a turning fork of frequency 886 Hz) when the tube length is 5 cm or 9 cm. Estimate the speed of sound in air.\n",
        "input": "wavelength = 4*length of tube, speed of sound = frequency*wavelength",
        "output": "1.77e+02 ms-1\nSince the given pipe is attached with a piston at one end, it will behave as a pipe with one end closed and the other end open. Such a system produces odd harmonics."
    },
    {
        "instruction": "A circular coil of wire consisting of 86 turns, each of radius 65 cm carries a current of 17 A. What is the magnitude of the magnetic field B at a point on the axis which is 40 cm from the center of the coil?",
        "input": "B = (mu * n * i * r^2) / (2 * sqrt((r^2 + x^2)^3))",
        "output": "To calculate the magnetic field B at a point on the axis, which is 40 cm from the center of the coil, we use the following formula:\n\nB = (mu * n * i * r^2) / (2 * sqrt((r^2 + x^2)^3))\n\nWhere,\n- B = Magnetic field at the point on the axis\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- n = Number of turns in the coil\n- i = Current flowing through the coil\n- r = Radius of the coil\n- x = Distance from the center of the coil to the point on the axis\n\nSubstituting the given values into the formula, we find that the magnitude of the magnetic field B is approximately 8.73e-04 tesla."
    },
    {
        "instruction": "Given observations (tuples of I (in A) and V (in V)): (39, 663), (9, 153), (15, 255), (23, 391), (26, 442), (27, 459); Determine whether the given conductor is an ohmic conductor or not.\n",
        "input": "",
        "output": "Yes, it is an ohmic conductor.\n"
    },
    {
        "instruction": "A rope of negligible mass is wound round a hollow sphere of mass 68 kg and radius 76 cm. What is the linear acceleration of the hollow sphere if the rope is pulled with a force of 92 N? Assume that there is no slipping.",
        "input": "Acceleration = Force / (k * mass * radius)",
        "output": "Acceleration = 92 N / (0.6666666666666666 * 68 kg * 76 cm)\n\nTo calculate the linear acceleration of the hollow sphere, we use the following formula:\n\nAcceleration = Force / (k * mass * radius)\n\nSubstituting the values:\n\nForce = 92 N\nk = 0.6666666666666666\nMass = 68 kg\nRadius = 76 cm\n\nWe find that the linear acceleration of the hollow sphere is approximately 2.0 m/s\u00b2."
    },
    {
        "instruction": "An object is placed at 1284 cm in front of a convex mirror. Image is formed at a distance of 380 cm behind it. Find the focal length of the mirror.",
        "input": "",
        "output": "540"
    },
    {
        "instruction": "A 9596 N force is applied on a body of mass 296 kg placed on a smooth surface, then what is the resulting acceleration obtained?",
        "input": "a = F / m",
        "output": "32.4\nTo calculate the acceleration, we use the formula a = F / m, where a is the acceleration, F is the force (9596 N), and m is the mass (296 kg)."
    },
    {
        "instruction": "A man can swim with a speed of 21 m/s in still water. How long does he take to cross a river 13 km wide if the river flows steadily at 150 m/s and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank, and what is the angle of deviation of his path from normal?",
        "input": "v1 = 21 m/s, v2 = 150 m/s, s = 13 km",
        "output": "The time taken is 619.0 seconds. The distance down the river is 13 km. The angle of deviation is 82 degrees."
    },
    {
        "instruction": "Two objects of masses 12 g and 8 g are moving along the same line and direction with velocities of 17 m/s and 3 m/s respectively. They collide and after the collision, the first object moves at a velocity of 2 m/s. Determine the initial velocity of the first object.",
        "input": "u1 = ((m1 * v1) + (m2 * v2) - (m2 * u2)) / m1",
        "output": "To find the initial velocity of the first object (u1), we use the formula:\n\nu1 = ((m1 * v1) + (m2 * v2) - (m2 * u2)) / m1\n\nSubstituting the given values, we have:\n\nu1 = ((12 * 2) + (8 * 26) - (8 * 3)) / 12\n\nSimplifying the expression gives us u1 = 8.0 m/s."
    },
    {
        "instruction": "What is the velocity of an object of mass 356 kg having kinetic energy of 499244 J?",
        "input": "v = sqrt((2 * KE) / m)",
        "output": "To calculate the velocity, we use the formula v = sqrt((2 * KE) / m), where v is the velocity, KE is the kinetic energy (499244 J), and m is the mass (356 kg)., this is the final answer 53.0"
    },
    {
        "instruction": "On an unknown scale, the temperature of the melting point and boiling point of water is -23 degrees and 191 degrees respectively. If the temperature on the Celsius scale is 85 degrees Celsius, what is the temperature shown on that scale?",
        "input": "Temperature on the unknown scale = (((t2 - t1) * (t - ta)) / (tb - ta)) + t1",
        "output": "To find the temperature on the unknown scale, we use the following formula:\n\nTemperature on the unknown scale = (((t2 - t1) * (t - ta)) / (tb - ta)) + t1\n\nSubstituting the given values into the formula, we find that the temperature on the unknown scale is approximately 158.9."
    },
    {
        "instruction": "A circular coil of wire consisting of 130 turns, each of radius 243 cm placed in a horizontal plane carries a current of 12 A in clockwise direction. What is the magnitude and direction of the magnetic field B at the center of the coil?",
        "input": "B = (mu * n * i) / (2 * r)",
        "output": "To calculate the magnetic field B at the center of the coil, we use the following formula:\n\nB = (mu * n * i) / (2 * r)\n\nWhere,\n- B = Magnetic field at the center of the coil\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- n = Number of turns in the coil\n- i = Current flowing through the coil\n- r = Radius of the coil\n\nSubstituting the given values into the formula, we find that the magnitude of the magnetic field B is approximately 4.03e-04 tesla vertically downwards."
    },
    {
        "instruction": "A concave lens produces a real image of height 94 cm at a distance of 8 cm from it of a real object having a height of 170 cm. At what distance is the object placed from the lens?",
        "input": "Formula: u = (ho * v) / hi",
        "output": "To find the distance at which the object is placed from the lens, we use the formula u = (ho * v) / hi, where u is the distance of the object from the lens, v is the distance of the image from the lens, ho is the height of the object, and hi is the height of the image. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 14.5 cm from the lens., this is the final The object is placed at a distance of 14.5 cm from the lens."
    },
    {
        "instruction": "The coefficient of volume expansion of glycerine is 0.0004900000000000001 K^-1. What is the change in its volume 100 m^3 for a rise in temperature from 12 degree C to 262 degree C?",
        "input": "Change in volume = d1 * a * (t2 - t1)",
        "output": "To find the change in volume, we use the following formula:\n\nChange in volume = d1 * a * (t2 - t1)\n\nSubstituting the given values into the formula, we find that the change in volume is approximately 12.25 m^3."
    },
    {
        "instruction": "A steady current of 535 A flows through a conductor, then calculate the number of electrons through any cross section of the conductor in 201 s?",
        "input": "n = (I * t) / e",
        "output": "6.7209375e+23\n\nThe number of electrons through any cross section of the conductor can be calculated using the formula: n = (I * t) / e, where I is the current, t is the time, and e is the charge of an electron."
    },
    {
        "instruction": "A hollow cylinder rolls down two different inclined planes of heights 13 cm and 20 cm and with angles of inclination of 20 and 34, on which it reaches the bottom with more speed?",
        "input": "speed = height / (k + 1)",
        "output": "To compare the speeds, we use the following formula:\n\nspeed = height / (k + 1)\n\nSubstituting the given values into the formula, we find that:\n\nThe second plane has more speed."
    },
    {
        "instruction": "A circular coil of radius 38 cm and 14 turns is rotated about its vertical diameter with an angular speed of 100 rad/s in a uniform horizontal magnetic field of magnitude 4.5 T. Obtain the maximum and average emf induced in the coil. If a coil forms a closed loop of resistance 7 ohm, what is the maximum current in the coil and average power loss due to joule heating?\n",
        "input": "EMF = n * w * b * A, I = EMF / R, P = (EMF * I) / 2",
        "output": "maximum emf: 2.86e+03 volt, average emf: 0 volts, maximum current: 4.08e+02 amp, average power loss: 5.83e+05 joule\n\n\nThe maximum emf induced in the coil can be calculated using the formula EMF = n * w * b * A, where n is the number of turns, w is the angular speed, b is the magnetic field magnitude, and A is the area of the coil.\nThe maximum current in the coil can be calculated using the formula I = EMF / R, where R is the resistance of the coil.\nThe average power loss due to joule heating can be calculated using the formula P = (EMF * I) / 2."
    },
    {
        "instruction": "An object of mass 1259 g stands on a weighing machine in a lift, which is moving downwards with a uniform acceleration of 910 cm/s^2.",
        "input": "Scale Reading = m * (10 - (acc / 100))",
        "output": "1.1\nTo calculate the scale reading, we use the formula Scale Reading = mass * (10 - (acceleration / 100)), where the mass is 1259 g and the acceleration is 910 cm/s^2."
    },
    {
        "instruction": "Four point charges q1 = 8 x 10^(-6) C, q2 = 19 x 10^(-6) C, q3 = 7 x 10^(-6) C, q4 = -8 x 10^(-6) C, are located at corners of square ABCD of side 17 cm. What is the force on a charge of -7 x 10^(-6) C placed at the centre of the square?\n",
        "input": "Force (F) = k * |q1 - q3| * |q2 - q4| * q_c / (d^2)",
        "output": "To calculate the force on the charge placed at the center of the square, we use the formula for electric force between two point charges:\nForce (F) = k * |q1 - q3| * |q2 - q4| * q_c / (d^2)\nwhere k is Coulomb's constant (9 * 10^9 N\u00b7m\u00b2/C\u00b2), q1, q2, q3, q4 are the charges at the corners of the square (in Coulombs), q_c is the charge placed at the center of the square (in Coulombs), and d is the side length of the square (in meters).\nGiven q1 = 8 x 10^(-6) C, q2 = 19 x 10^(-6) C, q3 = 7 x 10^(-6) C, q4 = -8 x 10^(-6) C, d = 17 cm, and q_c = -7 x 10^(-6) C:\nForce (F) = -5.89e+01 N\n"
    },
    {
        "instruction": "A bat emits ultrasonic sound of frequency 602488 Hz in air. If this sound meets a water surface, what is the wavelength of the transmitted sound? (Speed of sound in air = 340 ms-1 and in water = 1486 ms-1)\n",
        "input": "wavelength of transmitted sound = speed of sound in water/frequency of the ultrasonic sound",
        "output": "2.47e-03 m\nGiven that the speed of sound in air is 340 m/s and the speed of sound in water is 1486 m/s, we can substitute these values into the formula to calculate the wavelength. For the sound emitted in air: \u03bb_air = (340 m/s) / 602488 Hz, For the sound reflected in water: \u03bb_water = (1486 m/s) / 602488 Hz"
    },
    {
        "instruction": "What is the lowest total resistance that can be secured by combinations of three coils of resistance 45, 65, 32?",
        "input": "R_total = (R1 * R2 * R3) / (R1 * R2 + R2 * R3 + R3 * R1)",
        "output": "The lowest combination of resistances can be obtained by connecting them in parallel. The total resistance is calculated as (45 * 65 * 32) / (45 * 65 + 65 * 32 + 32 * 45) = 14.5 ohm.\n\nTo calculate the lowest combination of resistances, we connect them in parallel. The total resistance (R_total) is given by the formula (R1 * R2 * R3) / (R1 * R2 + R2 * R3 + R3 * R1), where R1, R2, and R3 are the individual resistances."
    },
    {
        "instruction": "Suppose that the electric field amplitude of an electromagnetic wave is E0 = 887 N/C and that its frequency is v = 1857 MHz. Determine B0?",
        "input": "E0 = 887 N/C",
        "output": "2.96e-06 tesla\n\nThe magnetic field amplitude can be determined by dividing the electric field amplitude by the speed of light."
    },
    {
        "instruction": "Estimate the fraction of molecular volume to the actual volume occupied by a gas at STP. Take the diameter of the gas molecule to be 997.8 A and volume occupied by a gas at STP as 22.4 L.",
        "input": "(4 * pi * d * d * d * 1000 * n) / (3 * 8 * 22.4)",
        "output": "1.3986014235835683e+34 \n (4 * pi * d * d * d * 1000 * n) / (3 * 8 * 22.4)"
    },
    {
        "instruction": "A stone is thrown vertically upward with an initial velocity of 1664 m/s and reaches the maximum height after 90 s. What is the maximum height attained by the stone?",
        "input": "initial velocity (u) = 1664 m/s, time (t) = 90 s",
        "output": "maximum height (h) = (initial velocity (u) * time (t)) + (0.5 * acceleration (a) * time (t)\u00b2)\nh = (1664 * 90) + (0.5 * 9.8 * 90\u00b2)\nh = 149760 + 39690.0\nh = 189450.0\nh = 189450.0"
    },
    {
        "instruction": "Two narrow bores of diameters 17 mm and 19 mm are joined together to form a U-tube open at both ends. If the U-tube contains an unknown liquid, what is the difference in its levels at two ends? Surface tension of liquid is 15 x 10^(-2) Nm-2. Take the angle of contact to be 108 degrees and density of liquid to be 5 x 10^3 kgm-3.",
        "input": "abs(-1.8919407818874327e-06 * 6.191950464396287)",
        "output": "The difference in levels of the U-tube is given by abs(-1.8919407818874327e-06 * 6.191950464396287). Substituting the given values, we have abs(-1.8919407818874327e-06 * 6.191950464396287) = 1.17e-05 m."
    },
    {
        "instruction": "A small bulb is placed at the bottom of a tank containing liquid to a depth of 40 cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of the liquid is 2.42.",
        "input": "Formula: Area = \u03c0 * h\u00b2 * (k / (1 - k)), where h is the depth of the liquid in centimeters, k is the reciprocal of the refractive index of the liquid, and k = 1 / mu.",
        "output": "This is the answer 0.1 m\u00b2, formula used is : Formula: Area = \u03c0 * h\u00b2 * (k / (1 - k)), where h is the depth of the liquid in centimeters, k is the reciprocal of the refractive index of the liquid, and k = 1 / mu."
    },
    {
        "instruction": "A steam engine delivers 39 J of work per minute and services 996 J of heat per minute from its boiler. How much heat is wasted per minute?\n",
        "input": "Efficiency = Work per minute/Heat per minute from its boiler, Heat Wasted = Heat per minute - (Efficiency/100)*Heat per minute",
        "output": "957 joules\nThe efficiency of an engine can be calculated using the formula: Efficiency = (Work output / Heat input) * 100"
    },
    {
        "instruction": "A convex lens produces a real image of height 43 cm at a distance of 57 cm from it of a real object having a height of 53 cm. At what distance is the object placed from the lens?",
        "input": "Formula: u = (v * ho) / hi",
        "output": "To find the distance at which the object is placed from the lens, we use the formula u = (v * ho) / hi, where u is the distance of the object from the lens, v is the distance of the image from the lens, hi is the height of the image, and ho is the height of the object. By substituting the given values into the formula, we can calculate u. In this case, the object is placed at a distance of 70.3 cm from the lens., this is the final The object is placed at a distance of 70.3 cm from the lens."
    },
    {
        "instruction": "What is the lowest total resistance that can be secured by combinations of three coils of resistance 43, 125, 46?",
        "input": "R_total = (R1 * R2 * R3) / (R1 * R2 + R2 * R3 + R3 * R1)",
        "output": "The lowest combination of resistances can be obtained by connecting them in parallel. The total resistance is calculated as (43 * 125 * 46) / (43 * 125 + 125 * 46 + 46 * 43) = 18.9 ohm.\n\nTo calculate the lowest combination of resistances, we connect them in parallel. The total resistance (R_total) is given by the formula (R1 * R2 * R3) / (R1 * R2 + R2 * R3 + R3 * R1), where R1, R2, and R3 are the individual resistances."
    },
    {
        "instruction": "A 65 muF capacitor in series with a 17 ohm resistance is connected to a 224 V, 61 Hz supply. What is the time lag between the current maximum and voltage maximum?",
        "input": "Time_lag = atan(1 / (f * C * 10^-6 * 2 * pi * R)) / (2 * pi * f)",
        "output": "3.05e-03 s"
    },
    {
        "instruction": "A capacitor with air between it's parallel plates, each plate has an area of 0.0484 m2 and the distance between the plates is 1843 mm. Calculate the capacitance of the capacitor?\n",
        "input": "C = (\u03b5\u2080 * A) / d",
        "output": "2.33e-01 pico-farad\n\n\n Explanation: To calculate the capacitance C of a capacitor with air between its parallel plates, we use the formula above. In the formula, \u03b5\u2080 represents the permittivity of free space, A represents the area of each plate, and d represents the distance between the plates. By multiplying the permittivity of free space by the plate area and dividing it by the plate separation, we can determine the capacitance of the capacitor"
    },
    {
        "instruction": "A stone is thrown vertically upward and reaches a maximum height of 919410 m. What is the initial velocity of the stone?",
        "input": "maximum height (h) = 919410 m",
        "output": "maximum height (h) = (initial velocity (u)\u00b2) / (2 * acceleration (g))\n919410 = (u\u00b2) / (2 * 9.8)\n919410 = u\u00b2 / 19.6\n919410 * 19.6 = u\u00b2\n18020436.0 = u\u00b2\n\u221a18020436.0 = u\nu = 4245.0"
    },
    {
        "instruction": "A person needs a lens of power -60733 dioptres for correcting his distant vision. What is the focal length of the lens required for correcting distant vision?\n",
        "input": "Power = 1/focal length (f)",
        "output": "we know that power(P)=1/f, hence f=1/P, f(in mm)=1000/P, hence f=0.02 mm\n"
    },
    {
        "instruction": "A refrigerator is to maintain eatables kept inside at -83 degree C, if room temperature is 65 degree C. Calculate the coefficient of performance.\n",
        "input": "Coefficient of performance = T2/T1-T2",
        "output": "1.3\nThis formula is only applicable if the refrigerator is based on the Carnot Cycle."
    },
    {
        "instruction": "About 34 percent of the power of a 380 W light bulb is converted to visible radiation. What is the average intensity of the visible radiation at a distance of 80 m from the bulb?\n",
        "input": "Average Intensity = (Percentage Power / Total Power) / (4 * pi * distance^2)",
        "output": "1.11e-04 watt/m2\n\n\nThe average intensity of the visible radiation at a distance 'd' from the bulb can be calculated using the formula Average Intensity = (Percentage Power / Total Power) / (4 * pi * distance^2), where Percentage Power is the percentage of power converted to visible radiation, Total Power is the total power of the light bulb, and 'd' is the distance from the bulb."
    },
    {
        "instruction": "A circuit consists of 4 V battery, 49 ohm resistance, then what is the heat energy produced in the circuit in 916 s?",
        "input": "Heat = (V^2 * t) / R",
        "output": "To calculate the heat energy produced in the circuit, we use the formula Heat = (V^2 * t) / R, where V is the voltage (4 V), t is the time (916 s), and R is the resistance (49 ohm)., this is the final answer 299.1"
    },
    {
        "instruction": "A 78 kg girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter 26629 micrometer. What is the pressure exerted by the heel on the horizontal floor?",
        "input": "78 * 9.8 / 0.0005569286972998435",
        "output": "The pressure exerted by the heel on the horizontal floor is 1.37e+06 newton. The pressure exerted by the heel on the horizontal floor is calculated using the formula P = (m * 9.8) / A, where m is the mass of the girl (78 kg) and A is the area of the heel (0.0005569286972998435 m^2)."
    },
    {
        "instruction": "In a process, change in internal energy of the system is 5857 J. If 6057 J of work is done on the system, what is the amount of heat absorbed by the process ?\n",
        "input": "\u0394U = Q+W",
        "output": "from first law of thermodynamics, du = q + w => q = du - w => q = (5857) - (+6057) => q = -200joule\n"
    },
    {
        "instruction": "Monochromatic light of wavelength of 2050 nm is incident on aa surface of refractive index 205.0. What is the wavelength, speed and frequenct of reflected light.\n",
        "input": "frequency = c/wavelength",
        "output": "2050.0 nm , 3.00e+08 m/s and 1.46e+14 hz \nThe ray will reflect back in the same medium as that of incident ray. Hence, the wavelength, speed, and frequency of the reflected ray will be the same as that of the incident ray."
    },
    {
        "instruction": "An infinite line charge produces a field of 8174 N/C at a distance of 30 cm. Calculate the linear charge density.\n",
        "input": "Linear charge density = (Electric field * distance) / (18 * epsilon_0)",
        "output": "To calculate the linear charge density, we use the formula:\nLinear charge density = (Electric field * distance) / (18 * epsilon_0)\nGiven electric field = 8174 N/C, distance = 30 cm,\nLinear charge density = 1.36e-07 C/m\n"
    },
    {
        "instruction": "The piston in the cylinder head of a locomotive has a stroke (9 times the amplitude) of 148 m. If the piston moves with SHM with an angular frequency of 604 rev/min, what its amplitude, maximum speed?\n",
        "input": "amp2 = amp/ratio, v = (freq*amp2)/60",
        "output": "amp2 = amp/ratio, v = (freq*amp2)/60  this is the final answer: amplitude is 1.64e+01 m, its maximum speed is 1.66e+02 ms-1\n"
    },
    {
        "instruction": "A sonar device on a submarine sends out a signal and receives an echo 705 s later. Find the distance of the object from the submarine if speed of sound in that material is 329 m/s ?\n",
        "input": "Distance = Speed * Time",
        "output": "115972.5 m\nTo find the distance of the object from the submarine, we can use the equation: Distance = Speed * Time. In this case, the speed of sound in the material is 329 m/s and the time it takes for the echo to return is 705 seconds. Substituting these values into the equation, we can calculate the distance of the object from the submarine: Distance = 329 m/s * 705 s. Calculating this expression will give us the distance of the object from the submarine."
    },
    {
        "instruction": "A helicopter of mass 1088 kg rises with a vertical acceleration of 16 m/s^2. The crew and the passengers weigh 319 kg. Give the magnitude and direction of",
        "input": "force on the helicopter due to the surrounding air",
        "output": "36582 newton, vertically upwards\n\nThe force on the helicopter due to the surrounding air can be calculated based on the given mass (1088 kg), weight of crew and passengers (319 kg), and acceleration (16 m/s^2)."
    },
    {
        "instruction": "Suppose we employ a system of units in which the unit of mass equals 41 kg, the unit of length equals 70 m, the unit of time is 57 s, then value of 73 joules in new system\n",
        "input": "73 J = (m kg) * (l m^2) / (t^2 s^2)",
        "output": "1.18\nTo find the value of 73 joules in the given system of units, we need to consider the relationships between the units of mass (kg), length (m), time (s), and energy (Joule). In the new system of units, we have: 1 unit of mass = 1.18\n kg, 1 unit of length = 70 m, 1 unit of time = 57 s. To find the value of 73 joules, we need to determine the conversion factors between the new system and the standard SI units. The energy (Joule) can be expressed as: 73 J = (m kg) * (l m^2) / (t^2 s^2). Substituting the given values into this equation, we have:73 J = (m * 1.18\n kg) * (l * 70 m^2) / (t^2 * 57 s^2). Simplifying this expression will give us the value of 73 joules in the new system of units."
    },
    {
        "instruction": "A hollow sphere of mass 575 kg rotates about its axis with angular speed 5 rad/s. The radius of the sphere is 7 m. What is the magnitude of angular momentum of the sphere about its axis?",
        "input": "Angular Momentum = c * m * r\u00b2 * w",
        "output": "To calculate the magnitude of the angular momentum, we use the following formula:\n\nAngular Momentum = c * m * r\u00b2 * w\n\nWhere,\n- c = Constant for the object\n- m = Mass of the object\n- r = Radius or length of the object\n- w = Angular speed of the object\n\nThe value of the constant (c) depends on the type of object being considered:\n- For a solid cylinder: c = 1/2\n- For a solid sphere: c = 2/5\n- For a hollow sphere: c = 2/3\n- For a rod: c = 1/3\n\nSubstituting the given values into the formula, we find that the magnitude of the angular momentum is approximately 93916.7 kg\u00b7m\u00b2."
    },
    {
        "instruction": "In a meter bridge, the balance point is found to be at 358 mm from end A, when the resistor Y is of 3652 ohm. Determine the balance point of the bridge above if X and Y are interchanged.",
        "input": "New balance point = 1000 - balance_point",
        "output": "642 mm\n\nExplanation: When X and Y are interchanged, the new balance point can be calculated by subtracting the current balance point from 1000."
    },
    {
        "instruction": "A child stands at the centre of a turntable with his arms outstretched. The turntable is rotating with an angular speed of 99 rad/s. How many times is the kinetic energy of the rotation increased if he folds his hands back and thereby reduces his moment of inertia to 68/119 times the initial value?",
        "input": "Angular Speed = (n2 * w) / n1\nKinetic Energy Ratio = (n2^3) / (n1^3)",
        "output": "To calculate the angular speed and kinetic energy ratio, we use the following formulas:\n\nAngular Speed = (n2 * w) / n1\nKinetic Energy Ratio = (n2^3) / (n1^3)\n\nWhere,\n- n1 = Initial moment of inertia\n- n2 = Reduced moment of inertia\n- w = Initial angular speed\n\nSubstituting the given values into the formulas, we find that the kinetic energy of the rotation is increased by approximately 5.4 times."
    },
    {
        "instruction": "If a gas of 5 moles at 55 m3 is isothermally changed to volume 52 m3 at 25 K, then what is the work done.\n",
        "input": "Work Done = n*R*T*ln(V2/V1)",
        "output": "58.3 joules\nTo calculate the work done during an isothermal expansion of a monoatomic gas, we can use the following equation: Work done = n * R * T * ln(V2/V1), where n is the number of moles of the gas, R is the ideal gas constant (approximately 8.314 J/(mol\u00b7K)), T is the temperature in Kelvin, V1 is the initial volume, and V2 is the final volume."
    },
    {
        "instruction": "If an artificial satellite is moving in a circular orbit of radius 2061 m, then calculate its speed if it takes 179 s to complete a rotation?",
        "input": "r = 2061 m, t = 179 s",
        "output": "The speed of the satellite is 72.3 m/s."
    },
    {
        "instruction": "A stone is thrown vertically upward with an initial velocity of 7689.34 m/s under gravity. What is the maximum height attained by the stone?",
        "input": "initial velocity (u) = 7689.34 m/s",
        "output": "maximum height (h) = (initial velocity (u)\u00b2) / (2 * acceleration (g))\nh = (7689.34\u00b2) / (2 * 9.8)\nh = 59125949.6356 / 19.6\nh = 3016630.1"
    },
    {
        "instruction": "A sound produces 280 crests and 280 troughs in 64 seconds. When the first trough is produced, the first crest is 1055 m away from the source, then calculate the frequency ?\n",
        "input": "Wavelength = Speed*Time Period, ",
        "output": "4.4 hz\nTo calculate the speed of sound, we need to determine the distance traveled by a crest or trough in the given time interval. In 64 seconds, 280 crests and 280 troughs are produced. This means that one complete cycle of the wave (a crest and a trough) occurs 280 times in 64 seconds. Therefore, the time taken for one complete cycle (T) can be calculated as: T = 64 s / 280 cycles. The distance traveled by one complete cycle (wavelength, \u03bb) is given by the formula: \u03bb = speed * T, where speed is the speed of sound. Since the first crest is 1055 m away from the source, the distance traveled by a complete cycle (\u03bb) can be expressed as: \u03bb = 1055 m + 1055 m = 2 * 1055 m. Substituting the value of \u03bb and T into the equation, we can calculate the speed of sound: speed = \u03bb / T = (2 * 1055 m) / (64 s / 280 cycles). Calculating this expression will give us the speed of sound."
    },
    {
        "instruction": "A U tube contains water and liquid separated by mercury. The mercury columns in the two arms are in level with 584 mm of water in one arm and 1744 mm of liquid in the other. What is the relative density of the liquid?",
        "input": "l2 / l1",
        "output": "Output: The relative density of the liquid is 2.99."
    },
    {
        "instruction": "In a harbour, wind is blowing at the speed of 2176 m/s and the flag on the mast of a boat anchored in the harbour flutters along the N-E direction. If the boat starts moving at a speed of 680 m/s to the north, what is the direction of the flag on the mast of the boat?",
        "input": "v1 = 2176 m/s, v2 = 680 m/s",
        "output": "29 degrees north of east"
    },
    {
        "instruction": "The piston in the cylinder head of a locomotive has a stroke (10 times the amplitude) of 85 m. If the piston moves with SHM with an angular frequency of 909 rev/min, what its amplitude, maximum speed?\n",
        "input": "amp2 = amp/ratio, v = (freq*amp2)/60",
        "output": "amp2 = amp/ratio, v = (freq*amp2)/60  this is the final answer: amplitude is 8.50e+00 m, its maximum speed is 1.29e+02 ms-1\n"
    },
    {
        "instruction": "A rope of negligible mass is wound round a solid sphere of mass 80 kg and radius 99 cm. What is the angular acceleration of the solid sphere if the rope is pulled with a force of 7 N? Assume that there is no slipping.",
        "input": "Acceleration = Force / (k * mass * radius)",
        "output": "Acceleration = 7 N / (0.4 * 80 kg * 99 cm)\n\nTo calculate the angular acceleration of the solid sphere, we use the following formula:\n\nAcceleration = Force / (k * mass * radius)\n\nSubstituting the values:\n\nForce = 7 N\nk = 0.4\nMass = 80 kg\nRadius = 99 cm\n\nWe find that the angular acceleration of the solid sphere is approximately 0.2 rad/s\u00b2."
    },
    {
        "instruction": "A sphere of radius 68 cm has an unknown charge. If the electric field at 153 cm from the center of the sphere is 690 N/C and points radially inward, then what is the net charge on the sphere?\n",
        "input": "Net charge = Electric field * (distance^2) * (1 / (4 * pi * epsilon_0))",
        "output": "-To calculate the net charge on the sphere, we use the formula:\nNet charge = Electric field * (distance^2) * (1 / (4 * pi * epsilon_0))\nGiven electric field = 690 N/C, distance = 153 cm,\nNet charge = 1.79e-03 C\n"
    },
    {
        "instruction": "Suppose that the electric field part of an electromagnetic wave in vacuum is E = 169cos[1248y + 240385t]. Write an expression for the magnetic field part of the wave?",
        "input": "B0 = 5.63e-07 tesla, k = 1248, w = 240385",
        "output": "5.63e-07cos[1248y + 240385t]\n\nThe expression for the magnetic field part of the wave can be written as B = B0cos[ky + wt]."
    },
    {
        "instruction": "In a chamber, a uniform magnetic field of 0.0031000000000000003 T is maintained. An electron is shot into the field with a speed of 76000000 m/s, making an angle of 61 degrees with the field. Determine the frequency of the revolution of the electron.",
        "input": "Frequency of revolution = (b * e) / (2 * pi * m)",
        "output": "To calculate the frequency of revolution, we use the following formula:\n\nFrequency of revolution = (b * e) / (2 * pi * m)\n\nSubstituting the given values:\n- b = 0.0031000000000000003 T\n- e = 1.6000000000000002e-19 C\n- m = 9.1e-31 kg\n\nAfter evaluating the formula, we find that the frequency of revolution is approximately 8.67e+07 sec^-1."
    },
    {
        "instruction": "A rope of negligible mass is wound round a solid sphere of mass 11 kg and radius 31 cm. What is the linear acceleration of the solid sphere if the rope is pulled with a force of 35 N? Assume that there is no slipping.",
        "input": "Acceleration = Force / (k * mass * radius)",
        "output": "Acceleration = 35 N / (0.4 * 11 kg * 31 cm)\n\nTo calculate the linear acceleration of the solid sphere, we use the following formula:\n\nAcceleration = Force / (k * mass * radius)\n\nSubstituting the values:\n\nForce = 35 N\nk = 0.4\nMass = 11 kg\nRadius = 31 cm\n\nWe find that the linear acceleration of the solid sphere is approximately 8.0 m/s\u00b2."
    },
    {
        "instruction": "A stone is thrown vertically upward and reaches a maximum height of 175757 m. What is the initial velocity of the stone?",
        "input": "maximum height (h) = 175757 m",
        "output": "maximum height (h) = (initial velocity (u)\u00b2) / (2 * acceleration (g))\n175757 = (u\u00b2) / (2 * 9.8)\n175757 = u\u00b2 / 19.6\n175757 * 19.6 = u\u00b2\n3444837.2 = u\u00b2\n\u221a3444837.2 = u\nu = 1856.0"
    },
    {
        "instruction": "Earthquakes generate sound waves inside the earth, assuming the speed of transverse(S) wave is 5960 ms-1, speed of longitudinal(P) wave is 6430 ms-1, if the first P wave arrives 324 s before the first S wave to seismograph, at what distance does the earthquake occur?\n",
        "input": "Vs*Ts=Vp*Tp, L = Vp*Tp",
        "output": "2.64e+04 km\nTo determine the distance to the earthquake epicenter, we can use the difference in arrival times between the P wave and S wave at the seismograph.Using the formula for distance (d) based on wave speed and time: d = (P wave speed - S wave speed) * t"
    },
    {
        "instruction": "An object is projected with an initial velocity of 842 m/s, if the horizontal range of the object is 10892 m, what is the angle of projection?",
        "input": "v = 842 m/s, h = 10892 m",
        "output": "4, 86"
    },
    {
        "instruction": "A body describes simple harmonic motion with an amplitude of 86 mm and a period of 132 ms. Find the velocity of the body when the displacement is 36 mm?\n",
        "input": "w*math.sqrt(amp1**2-amp**2)",
        "output": "Using this formula: w*math.sqrt(amp1**2-amp**2), this is the final answer derived: 3.72e+03 ms-1\n"
    },
    {
        "instruction": "A convex lens produces 23 times diminished real image of a 67.05 cm object placed in front of it. What is the height of the image formed by the lens?",
        "input": "Formula: hi = ho / n",
        "output": "To find the height of the image formed by the lens, we use the formula hi = ho / n, where hi is the height of the image, ho is the height of the object, and n is the magnification factor. By substituting the given values into the formula, we can solve for hi. In this case, the height of the image formed by the lens is 2.9 cm., this is the final The height of the image formed by the lens is 2.9 cm."
    },
    {
        "instruction": "A series LCR circuit is connected to a variable frequency 230 V source with L = 102 H, C = 59 muF, R = 118 ohm. Determine the source frequency which drives the circuit in resonance?",
        "input": "Source Frequency = 1 / sqrt(L * C)",
        "output": "12.9 rad/s"
    },
    {
        "instruction": "A convex mirror produces a real image of height 934 cm of a real object of height 1907 cm placed in front of it. What is the magnification of the mirror?",
        "input": "Formula: m = hi / ho = v / u",
        "output": "To find the magnification of the convex mirror, we use the formula m = hi / ho = v / u, where m is the magnification, hi is the height of the image, ho is the height of the object, v is the distance of the image from the mirror, and u is the distance of the object from the mirror. Since the heights are provided instead of distances, the formula still holds. By substituting the given values into the formula, we can calculate the magnification. In this case, the magnification of the mirror is 0.5., this is the final The magnification of the mirror is 0.5."
    },
    {
        "instruction": "Monochromatic light of wavelength of 8006 nm is incident on aa surface of refractive index 800.6. What is the wavelength, speed and frequenct of reflected light.\n",
        "input": "frequency = c/wavelength",
        "output": "8006.0 nm , 3.00e+08 m/s and 3.75e+13 hz \nThe ray will reflect back in the same medium as that of incident ray. Hence, the wavelength, speed, and frequency of the reflected ray will be the same as that of the incident ray."
    },
    {
        "instruction": "An object is placed at 905 cm in front of a convex lens of focal length 113 cm. Find at what distance image is formed and its nature.",
        "input": "Formula: 1/f = 1/v - 1/u for convex lens.",
        "output": "To find the distance of the image formed, we use the formula for convex lenses: 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for v. In this case, the image is real and located at a distance of 129.1 cm., this is the final The image is formed at 129.1 cm and it is real."
    },
    {
        "instruction": "In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are 73 ms-1 and 58 ms-1. What is the lift on the wing if its area is 11100 cm2?",
        "input": "0.5 * 1.3 * (73**2 - 58**2) * (11100 / 10000)",
        "output": "The lift on the wing is 1417.7475000000002 newton."
    },
    {
        "instruction": "A meter stick of mass 21 g is balanced on a knife edge at its center. Where will the stick be balanced when a coin of mass 53 g is put at the 15 mark?",
        "input": "Balance Position = ((50 * m) + (m1 * t1)) / (m + m1)",
        "output": "The stick will be balanced at approximately 24.9 cm.\nBalance Position = ((50 * 21) + (53 * 15)) / (21 + 53)"
    },
    {
        "instruction": "A truck starts from rest and accelerates uniformly at 9 ms-2. At t = 34 s, a stone is dropped by a person standing on the top of the truck (14 m high from the ground). What are the (a) velocity, and (b) acceleration of the stone at t = 64 s? (Neglect air resistance.)",
        "input": "A truck starts from rest and accelerates uniformly at 9 ms-2. At t = 34 s, a stone is dropped by a person standing on the top of the truck (14 m high from the ground). What are the (a) velocity, and (b) acceleration of the stone at t = 64 s? (Neglect air resistance.)",
        "output": "Velocity is 428.5 ms-1, at an angle of 44 degrees with horizontal. Acceleration is g (10 ms-2) downwards."
    },
    {
        "instruction": "The peak voltage of an ac supply is 148511 mV. What is the rms voltage?",
        "input": "RMS Voltage = Peak Voltage / sqrt(2)",
        "output": "1.050e+02 volt"
    },
    {
        "instruction": "Two objects of masses 4 g and 3 g are moving along the same line and direction with velocities of 2 m/s and 10 m/s respectively. They collide and after the collision, the second object moves at a velocity of 19 m/s. Determine the velocity of the first object.",
        "input": "v1 = ((m1 * u1) + (m2 * u2) - (m2 * v2)) / m1",
        "output": "To find the velocity of the first object (v1), we use the formula:\n\nv1 = ((m1 * u1) + (m2 * u2) - (m2 * v2)) / m1\n\nSubstituting the given values, we have:\n\nv1 = ((4 * 2) + (3 * 10) - (3 * 19)) / 4\n\nSimplifying the expression gives us v1 = -4.8 m/s."
    },
    {
        "instruction": "A disc revolves with a speed of 35 rpm and has a radius of 1 m. Two coins are placed at 17 cm (coin-1) and 23 cm (coin-2) away from the center of the record. If the coefficient of friction between the coins and the record is 0.61, which of the coins will revolve with the record?",
        "input": "Centripetal acceleration (a) = (\u03c0 / 30) * rot_speed\nOptimal radius (r_opt) = ((\u03bc * g) / (w * w)) * 100",
        "output": "coin1 will revolve,coin2 will revolve"
    },
    {
        "instruction": "A concave lens produces a real image of height 5 cm at a distance of 29 cm from it of a real object placed 112 cm in front of it. What is the height of the object?",
        "input": "Formula: ho = (hi * u) / v",
        "output": "To find the height of the object, we use the formula ho = (hi * u) / v, where ho is the height of the object, hi is the height of the image, u is the distance of the object from the lens, and v is the distance of the image from the lens. By substituting the given values into the formula, we can solve for ho. In this case, the height of the object is 19.3 cm., this is the final The height of the object is 19.3 cm."
    },
    {
        "instruction": "If a monoatomic gas of 2 moles at 42 pas is isothermally changed to pressure 46 pas at 33 K, then what is the work done.\n",
        "input": "Work Done = n*R*T*ln(P1/P2)",
        "output": "49.9 joules\nTo calculate the work done during an isothermal expansion of a monoatomic gas, we can use the following equation: Work done = n * R * T * ln(P1/P2), where n is the number of moles of the gas, R is the ideal gas constant (approximately 8.314 J/(mol\u00b7K)), T is the temperature in Kelvin, P1 is the initial pressure, and P2 is the final pressure."
    },
    {
        "instruction": "In a double-slit experiment the angular width of a fringe is found to be 0.5 degrees on a screen placed 6 m away. The wavelength of light used is 44 nm. What will be the angular width of the fringe if the entire experimental apparatus is immersed in liquid of refractive index 1.27.\n",
        "input": "refractive index = angular width before immersing in water/angular width after immersing in water",
        "output": "3.94e-01 degrees\nTo calculate the angular width of a fringe when the entire experimental apparatus is immersed in a liquid of refractive index (\u03bc), we need to consider the effect of the refractive index on the wavelength of light.we can calculate the angular width of the fringe in the liquid (\u03b82') using the formula: \u03b82' = sin^(-1)(\u03bb' / d), where d is the distance to the screen (D) in meters."
    },
    {
        "instruction": "Two masses each of mass 158 kg are attached by a spring with K = 175 Nm-1. If a force of 28 N is applied at the free ends of both masses, then what is the time period of oscillation?",
        "input": "Formula: T = 2\u03c0\u221a(m / (2k)), where T is the time period of oscillation, m is the mass of each mass (158 kg), and k is the spring constant (175 Nm-1).",
        "output": "Using this formula: Formula: T = 2\u03c0\u221a(m / (2k)), where T is the time period of oscillation, m is the mass of each mass (158 kg), and k is the spring constant (175 Nm-1)., this is the final answer derived: 4.22e+00 s"
    },
    {
        "instruction": "A rigid bar of mass 5 kg is supported symmetrically by three wires each 2 m long. Those at each end are of material-1 and the middle one is of material-2. Find ratios of their diameters all have the same tension (Young's modulus of material-1 is 1 x 10^9 Nm-2, material-2 is 30 x 10^9 Nm-2).",
        "input": "diameter_ratio = sqrt(Y2 / Y1)",
        "output": "The ratio of their diameters is 5.48."
    },
    {
        "instruction": "Two discs of moments of inertia 77 and 73 about their respective axes, and rotating with angular speed 59 rad/s and 62 rad/s are brought into contact face to face with their axes of rotation coincident. What is the angular speed of the two-disc system?",
        "input": "Angular Speed = ((i1 * w1) + (i2 * w2)) / (i1 + i2)\nLoss in Kinetic Energy = k1 + k2 - k\n\nk1 = 0.5 * i1 * w1^2\nk2 = 0.5 * i2 * w2^2\nk = 0.5 * (i1 + i2) * w^2",
        "output": "To calculate the angular speed and loss in kinetic energy, we use the following formulas:\n\nAngular Speed = ((i1 * w1) + (i2 * w2)) / (i1 + i2)\nLoss in Kinetic Energy = k1 + k2 - k\n\nWhere,\n- i1 = Moment of inertia of the first disc\n- i2 = Moment of inertia of the second disc\n- w1 = Angular speed of the first disc\n- w2 = Angular speed of the second disc\n\nSubstituting the given values into the formulas, we find that the angular speed of the two-disc system is approximately 60.5 rad/s rad/s"
    },
    {
        "instruction": "The edge of a cube is 108 cm long. One face of the cube is firmly fixed to a vertical wall. A mass of 150 kg is then attached to the opposite face of the cube. The shear modulus of the material of the cube is 150 GPa. What is the vertical deflection of this face?",
        "input": "deflection = (mass * 9.8) / (Y * 10^9 * (edge_length * 10^-2))",
        "output": "To calculate the vertical deflection, we use the formula:\n\ndeflection = (mass * 9.8) / (Y * 10^9 * (edge_length * 10^-2))\n   = (150 kg * 9.8) / (150 * 10^9 GPa * (108 cm * 10^-2 m/cm))\n   = 9.1 nm."
    },
    {
        "instruction": "Two discs of moments of inertia 60 and 59 about their respective axes, and rotating with angular speed 28 rad/s and 58 rad/s are brought into contact face to face with their axes of rotation coincident. What is the loss in kinetic energy of the two-disc system?",
        "input": "Angular Speed = ((i1 * w1) + (i2 * w2)) / (i1 + i2)\nLoss in Kinetic Energy = k1 + k2 - k\n\nk1 = 0.5 * i1 * w1^2\nk2 = 0.5 * i2 * w2^2\nk = 0.5 * (i1 + i2) * w^2",
        "output": "To calculate the angular speed and loss in kinetic energy, we use the following formulas:\n\nAngular Speed = ((i1 * w1) + (i2 * w2)) / (i1 + i2)\nLoss in Kinetic Energy = k1 + k2 - k\n\nWhere,\n- i1 = Moment of inertia of the first disc\n- i2 = Moment of inertia of the second disc\n- w1 = Angular speed of the first disc\n- w2 = Angular speed of the second disc\n\nSubstituting the given values into the formulas, we find that the loss in kinetic energy is approximately 13386.6 joules joules."
    },
    {
        "instruction": "A solid sphere of mass 764 kg rotates about its axis with angular speed 3 rad/s. The radius of the sphere is 1 m. What is the magnitude of angular momentum of the sphere about its axis?",
        "input": "Angular Momentum = c * m * r\u00b2 * w",
        "output": "To calculate the magnitude of the angular momentum, we use the following formula:\n\nAngular Momentum = c * m * r\u00b2 * w\n\nWhere,\n- c = Constant for the object\n- m = Mass of the object\n- r = Radius or length of the object\n- w = Angular speed of the object\n\nThe value of the constant (c) depends on the type of object being considered:\n- For a solid cylinder: c = 1/2\n- For a solid sphere: c = 2/5\n- For a hollow sphere: c = 2/3\n- For a rod: c = 1/3\n\nSubstituting the given values into the formula, we find that the magnitude of the angular momentum is approximately 916.8 kg\u00b7m\u00b2."
    },
    {
        "instruction": "A regular 9-gon with a distance between each vertex and the center as 164 cm has a charge of 231 micro-Coulombs at each of its vertices. Calculate the potential at the center of the 9-gon?",
        "input": "Formula: 9 * 10^9 * n * (q1 * 10^(-6)) * (1 / (d * 0.01))\nValues: n = 9, q1 = 231 micro-C, d = 164 cm",
        "output": "Answer: 1.14e+07 volt\n\nExplanation:\nThe potential at the center of the 9-gon can be calculated using the formula:\n\nV = k * n * q1 / d\n\nwhere k is the electrostatic constant (9 * 10^9 Nm^2/C^2), n is the number of vertices, q1 is the charge at each vertex, and d is the distance between each vertex and the center.\n\nSubstituting the given values, we have:\n\nV = 9 * 10^9 * 9 * (231 * 10^(-6)) / (164 * 0.01) = 1.14e+07 volt"
    },
    {
        "instruction": "A circular coil of wire consisting of 168 turns, each of radius 583 cm carries a current of 2 A. What is the magnitude of the magnetic field B at the center of the coil?",
        "input": "B = (mu * n * i) / (2 * r)",
        "output": "To calculate the magnetic field B at the center of the coil, we use the following formula:\n\nB = (mu * n * i) / (2 * r)\n\nWhere,\n- B = Magnetic field at the center of the coil\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- n = Number of turns in the coil\n- i = Current flowing through the coil\n- r = Radius of the coil\n\nSubstituting the given values into the formula, we find that the magnitude of the magnetic field B is approximately 3.62e-05 tesla."
    },
    {
        "instruction": "A pair of adjacent coils has a mutual inductance of 6.5 H. If the current in one coil changes from 28 A to 21 A in 7.6 sec, what is the change of flux linkage with the other coil?\n",
        "input": "Change in Flux Linkage = (Mutual Inductance * (Current 1 - Current 2)) / Time",
        "output": "5.99 weber\n\n\nThe change of flux linkage with the other coil can be calculated using the formula Change in Flux Linkage = (Mutual Inductance * (Current 1 - Current 2)) / Time, where Mutual Inductance is the mutual inductance of the coils, Current 1 and Current 2 are the initial and final currents respectively, and Time is the time taken for the change in current to occur."
    },
    {
        "instruction": "A rod of mass 3810 kg has a length of 80 m. What is the moment of inertia with respect to its center?",
        "input": "Moment of Inertia = (Constant) * mass * length^2",
        "output": "The moment of inertia with respect to its center is approximately 2032000.0 kgm^2.\n\nMoment of Inertia = (Constant) * mass * length^2\n\nConstant = 0.08333333333333333\nmass = 3810 kg\nlength = 80 m"
    },
    {
        "instruction": "If a gas of 8 moles at 23 m3 is isothermally changed to volume 38 m3 at 36 K, then what is the work done.\n",
        "input": "Work Done = n*R*T*ln(V2/V1)",
        "output": "-1201.6 joules\nTo calculate the work done during an isothermal expansion of a monoatomic gas, we can use the following equation: Work done = n * R * T * ln(V2/V1), where n is the number of moles of the gas, R is the ideal gas constant (approximately 8.314 J/(mol\u00b7K)), T is the temperature in Kelvin, V1 is the initial volume, and V2 is the final volume."
    },
    {
        "instruction": "To maintain a rotor at a uniform angular speed of 705 rad/s, an engine requires a power of 677 W. What is the torque transmitted by the engine?",
        "input": "Torque = Power / Angular Speed",
        "output": "Torque = 677 W / 705 rad/s\n\nTo calculate the torque transmitted by the engine, we use the following formula:\n\nTorque = Power / Angular Speed\n\nSubstituting the values:\n\nPower = 677 W\nAngular Speed = 705 rad/s\n\nWe find that the torque transmitted by the engine is 1.0 Nm."
    },
    {
        "instruction": "The edge of a cube is 140 cm long. One face of the cube is firmly fixed to a vertical wall. A mass of 150 kg is then attached to the opposite face of the cube. The shear modulus of the material of the cube is 164 GPa. What is the vertical deflection of this face?",
        "input": "deflection = (mass * 9.8) / (Y * 10^9 * (edge_length * 10^-2))",
        "output": "To calculate the vertical deflection, we use the formula:\n\ndeflection = (mass * 9.8) / (Y * 10^9 * (edge_length * 10^-2))\n   = (150 kg * 9.8) / (164 * 10^9 GPa * (140 cm * 10^-2 m/cm))\n   = 6.4 nm."
    },
    {
        "instruction": "What is the focal length of a concave lens of focal length 444 cm in contact with a convex lens of focal length 346 cm? Is the system a converging or a diverging lens? Ignore thickness of the lenses.",
        "input": "Formula: For two lenses in contact, the combined focal length (P) is given by P = (f1 * f2) / (f1 + f2), where f1 and f2 are the focal lengths of the lenses.",
        "output": "This is the answer {answer}, formula used is : {formula}"
    },
    {
        "instruction": "Suppose we employ a system of units in which the unit of mass equals 69 kg, the unit of length equals 59 m, the unit of time is 71 s, if the value of x newton is equal to 8 units in new system, find x?\n",
        "input": "x N = (m kg) * (l m) / (t^2 s^2)",
        "output": "6.46\nTo find the value of x newtons in the given system of units, we need to consider the relationships between the units of mass (kg), length (m), time (s), and force (Newton). In the new system of units, we have: 1 unit of mass = 6.46\n kg, 1 unit of length = 59 m, 1 unit of time = 71 s. To find the value of x newtons, we need to determine the conversion factors between the new system and the standard SI units. The force (Newton) can be expressed as: x N = (m kg) * (l m) / (t^2 s^2). Substituting the given values into this equation, we have: x N = (m * 6.46\n kg) * (l * 59 m) / (t^2 * 71 s^2). Simplifying this expression will give us the value of x in newtons."
    },
    {
        "instruction": "Two bodies A, B of masses 90 kg and 44 kg respectively kept on a smooth, horizontal surface are tied to the ends of a tight string. A horizontal force F = 215 N is applied to B along the direction of the string. What is the acceleration and tension in the string?",
        "input": "",
        "output": "The acceleration is 1.6 m/s^2, and the tension is 144.4 N."
    },
    {
        "instruction": "A bat is flitting about in a cave, navigating via ultrasonic beeps. Assume that the sound emission frequency of the bat is 44190 Hz. During one fast swoop directly toward a flat wall surface, the bat is moving at 0.1859 times the speed of sound in air. What is the apparent frequency of the sound striking the wall?\n",
        "input": "apparent frequency = [{(speed of air + speed of bat)}/speed of air]*apparent frequency of sound striking the wall",
        "output": "5.43e+04 hertz\nThe concept of Doppler's effect has been applied to calculate apparent frequencies."
    },
    {
        "instruction": "If a point on the circumference of a wheel rotating with an angular acceleration of 459 rad/s\u00b2 has an acceleration of 736 m/s\u00b2, what is the radius of the wheel?",
        "input": "radius = acceleration / angular_acceleration",
        "output": "To calculate the radius, we use the following formula:\n\nradius = acceleration / angular_acceleration\n\nSubstituting the given values into the formula, we find that the radius is approximately 1.6 m."
    },
    {
        "instruction": "Suppose we employ a system of units in which the unit of mass equals 48 kg, the unit of length equals 31 m, the unit of time is 96 s, then value of 43 joules in new system\n",
        "input": "43 J = (m kg) * (l m^2) / (t^2 s^2)",
        "output": "8.59\nTo find the value of 43 joules in the given system of units, we need to consider the relationships between the units of mass (kg), length (m), time (s), and energy (Joule). In the new system of units, we have: 1 unit of mass = 8.59\n kg, 1 unit of length = 31 m, 1 unit of time = 96 s. To find the value of 43 joules, we need to determine the conversion factors between the new system and the standard SI units. The energy (Joule) can be expressed as: 43 J = (m kg) * (l m^2) / (t^2 s^2). Substituting the given values into this equation, we have:43 J = (m * 8.59\n kg) * (l * 31 m^2) / (t^2 * 96 s^2). Simplifying this expression will give us the value of 43 joules in the new system of units."
    },
    {
        "instruction": "The escape speed of a projectile on the Earth's surface is 11.2 km/s. A body is projected out with the speed of 193.103 km/s. What is the speed of the body far away from the Earth?",
        "input": "Projectile Speed : 192.8 km/s km/s",
        "output": "192.8 km/s\n\nExplanation: The speed of the body far away from the Earth, when projected with a speed of 192.8 km/s km/s, can be calculated using the escape speed formula. By substituting the given values, the speed is found to be 192.8 km/s."
    },
    {
        "instruction": "An aircraft executes a horizontal loop of radius 1579 m with a steady speed of 382 m/s. Compare its centripetal acceleration with the acceleration due to gravity.",
        "input": "a = v\u00b2/r, g = 9.8 m/s\u00b2",
        "output": "centripetal acceleration is 92.4 ms-2, ratio is 9.4, g = 9.8 ms-2\n {explanation}"
    },
    {
        "instruction": "At what height should an object of mass 849 kg be placed such that its potential energy is 9023 J?",
        "input": "h = PE / (m * g)",
        "output": "To calculate the height, we use the formula h = PE / (m * g), where h is the height, PE is the potential energy (9023 J), m is the mass (849 kg), and g is the acceleration due to gravity (9.8 m/s^2)., this is the final answer 1.1"
    },
    {
        "instruction": "A capacitor with air between it's parallel plates, each plate has an area of 0.0736 m2 and the distance between the plates is 47 mm, if this capacitor is connected to a 359 V supply and a 47 mm thick mica sheet is inserted between the plates and then supply is disconnected, then what will happen?\n",
        "input": "C' = \u03b5r * C",
        "output": "capacitance becomes 8.32e+01 pico-farad, charge remains 4.98e-09 coulomb\n\nWhen a dielectric substance such as a mica sheet is inserted between the plates of a capacitor, the capacitance of the capacitor increases according to the formula above. In the formula, C' represents the new capacitance with the dielectric substance, \u03b5r represents the relative permittivity or dielectric constant of the material, and C represents the original capacitance without the dielectric substance. The relative permittivity of the dielectric material represents how much the electric field is intensified within the dielectric compared to free space. \n\nIn the given question, if a capacitor with air between its parallel plates, each plate having an area of A m\u00b2 and a distance of d mm, is connected to a V V supply and a d mm thick mica sheet is inserted between the plates, the capacitance C' of the capacitor will change according to the formula mentioned above"
    },
    {
        "instruction": "A copper wire has a cross-sectional area of 48 m\u00b2 and resistivity of 86 ohm-m. What is the length of this wire that makes its resistance 65 ohm?",
        "input": "R = 65 ohm, A = 48 m\u00b2, rho = 86 ohm-m",
        "output": "The length of the wire required to achieve a resistance of 65 ohm is 36.3 m. It is calculated by dividing the product of resistance and area (3120) by the resistivity (86)."
    },
    {
        "instruction": "For the travelling harmonic wave y(x, t) = 14 cos 2\u03c0 (50t \u2013 0.034x + 0.35) where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of 1\u03bb/5 ?\n",
        "input": "Phase difference = (2pi/wavelength)* Path difference",
        "output": "0.4 \u03c0 rad\nTo calculate the phase difference between two points in a traveling harmonic wave, we need to compare the phase angles of the wave at those points.In the given wave equation, the phase angle is represented by the term inside the cosine function, i.e., 2\u03c0(wt - kx + 0.35), where w represents the angular frequency and k represents the wave number.Let's assume the two points are at x1 and x2, separated by a distance \u0394x = x2 - x1. The phase difference between the oscillatory motion of these two points can be calculated using the equation: Phase difference = 2\u03c0(k\u0394x)"
    },
    {
        "instruction": "What is the electric field at a point P at a distance of 215 m from the center of the uniform solid sphere of radius 195 m and having 5.60e-07 C charge distributed uniformly.",
        "input": "Electric Field (E) = cal2(5.60e-07, 215, 195) N/C",
        "output": "1.09e-01 newton/coulomb\nThe electric field inside a uniformly charged solid sphere is given by the formula E = k * Q * r / (R^2), where k is the Coulomb's constant, Q is the charge on the sphere, r is the distance from the center, and R is the radius of the sphere. Plugging in the values, we get E = 1.09e-01 N/C."
    },
    {
        "instruction": "What is the gravitational potential at a point P on the surface of the spherical shell of radius 10 m and having 2.79e+02 C charge distributed uniformly on it.\n",
        "input": "To calculate the gravitational potential at a point on the surface of a uniformly charged spherical shell, we use the formula:\n\nV = (k * Q) / r\n\nwhere V is the gravitational potential, k is the electrostatic constant (9 * 10^9 Nm^2/C^2), Q is the charge, and r is the distance from the center of the shell.",
        "output": "2.51e+11 joule/coulomb\n"
    },
    {
        "instruction": "A large steel wheel is to be fitted onto a shaft of the same material. At 171 degree C, the outer diameter of the shaft is 130 cm and the diameter of the central hole in the wheel is 129.98 cm. The shaft is cooled using 'dry ice'. At what temperature of the shaft does the wheel slip on the shaft? Assume the coefficient of linear expansion of the steel to be constant over the required temperature range \u03b1steel = 1.20 x 10-5K-1.",
        "input": "Required temperature = t1 + ((d2 - d1) / (\u03b1 * d1))",
        "output": "To calculate the required temperature, we use the following formula:\n\nRequired temperature = t1 + ((d2 - d1) / (\u03b1 * d1))\n\nSubstituting the given values into the formula, we find that the temperature is approximately 158.2 degree C."
    },
    {
        "instruction": "If a physical quantity P=(a^-2.0)*(b^0.5)*(c^0.0), the percentage errors of measurement in a,b,c are 2%,2%,3% respectively. If the calculated value of P is 21 then what is maximum error possible.\n",
        "input": "Percentage Error in P = |dP/P| * 100",
        "output": "1.05\nTo find the maximum possible error in the calculated value of P, we can use the concept of percentage error propagation. The formula to calculate the percentage error in a quantity calculated from measured quantities is given by: Percentage Error in P = |dP/P| * 100, where dP is the maximum absolute error in P. Since P = (a^-2.0)*(b^0.5)*(c^0.0), we can differentiate the expression with respect to each measured quantity (a, b, c) to find the maximum absolute error for each term. Then we can substitute the given percentage errors and calculated value of P to find the maximum error. Let's calculate the maximum error using the given information."
    },
    {
        "instruction": "A concave lens produces a real image of height 24 cm of a real object having a height of 51 cm and placed 93 cm in front of it. At what distance is the image formed from the lens?",
        "input": "Formula: v = (u * hi) / ho",
        "output": "To find the distance at which the image is formed from the lens, we use the formula v = (u * hi) / ho, where v is the distance of the image from the lens, u is the distance of the object from the lens, hi is the height of the image, and ho is the height of the object. By substituting the given values into the formula, we can solve for v. In this case, the distance at which the image is formed from the lens is 43.8 cm., this is the final The distance at which the image is formed from the lens is 43.8 cm."
    },
    {
        "instruction": "If a monoatomic gas of 7 moles at 156 atm and volume 144 lit is adiabatically changed to volume 78 lit, then what will be the pressure.\n",
        "input": "P1*(V1^1.66)=P2*(V2^1.66)",
        "output": "431.6atm\nTo calculate the final pressure of the monoatomic gas after an adiabatic expansion, we can use the adiabatic equation: P1 * V1^\u03b3 = P2 * V2^\u03b3, where P1 and V1 are the initial pressure and volume, P2 and V2 are the final pressure and volume, and \u03b3 is the heat capacity ratio. The heat capacity ratio (\u03b3) for a monoatomic gas is typically 5/3."
    },
    {
        "instruction": "A particle has a velocity of 9010 m/s and wavelength 2.812e-07 A. Find its mass.\n",
        "input": "Mass = h/wavelength*velocity",
        "output": "0.0kg\nTo find the mass of the particle, we can use the de Broglie wavelength equation: \u03bb = h / (m * v) where \u03bb is the wavelength, h is the Planck constant (approximately 6.626 x 10^-34 J\u00b7s), m is the mass of the particle, and v is its velocity."
    },
    {
        "instruction": "A convex lens produces 50 times diminished real image of an object at a distance of 42.31 cm from the lens. At what distance is the object placed in front of the lens?",
        "input": "Formula: u = v * n",
        "output": "To find the distance at which the object is placed in front of the lens, we use the formula u = v * n, where u is the distance of the object from the lens, v is the distance of the image from the lens, and n is the magnification factor. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 2115.5 cm in front of the lens., this is the final The object is placed at a distance of 2115.5 cm in front of the lens."
    },
    {
        "instruction": "An Electric bulb of resistance 79 ohm produces heat at 1 W for 858 s. Calculate the potential difference maintained at service mains?",
        "input": "V = sqrt(P * R)",
        "output": "8.9 volt\n\nThe potential difference maintained at service mains can be calculated using the formula: V = sqrt(P * R), where P is the power and R is the resistance."
    },
    {
        "instruction": "A man can swim with a speed of 142 m/s in still water. How long does he take to cross a river 45 km wide if the river flows steadily at 172 m/s and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank, and what is the angle of deviation of his path from normal?",
        "input": "v1 = 142 m/s, v2 = 172 m/s, s = 45 km",
        "output": "The time taken is 316.9 seconds. The distance down the river is 45 km. The angle of deviation is 50 degrees."
    },
    {
        "instruction": "Suppose we employ a system of units in which the unit of mass equals 149 kg, the unit of length equals 90 m, the unit of time is 20 s, then value of 2 pascal in new system\n",
        "input": "2 Pa = (Force N) / (Area m\u00b2) = [(m kg) * (l m) / (t\u00b2 s\u00b2)] / [(l m)\u00b2]",
        "output": "483.22\nTo find the value of 2 pascals in the given system of units, we need to consider the relationships between the units of mass (kg), length (m), time (s), and pressure (Pascal). In the new system of units, we have: 1 unit of mass = 483.22\n kg, 1 unit of length = 90 m, 1 unit of time = 20 s. To find the value of 2 pascals, we need to determine the conversion factors between the new system and the standard SI units. The pressure (Pascal) can be expressed as: 2 Pa = (Force N) / (Area m\u00b2) = [(m kg) * (l m) / (t\u00b2 s\u00b2)] / [(l m)\u00b2] = (m * 483.22\n kg) / (t\u00b2 * 20 s\u00b2). Substituting the given values into this equation, we have: 2 Pa = (m * 483.22\n kg) / (t\u00b2 * 20 s\u00b2). Simplifying this expression will give us the value of 2 pascals in the new system of units."
    },
    {
        "instruction": "A 3m long tube open at one end, with a movable piston at the other end, shows resonance with a fixed frequency source (a turning fork of frequency 744 Hz) when the tube length is 54 cm or 169 cm. Estimate the speed of sound in air.\n",
        "input": "wavelength = 4*length of tube, speed of sound = frequency*wavelength",
        "output": "1.61e+03 ms-1\nSince the given pipe is attached with a piston at one end, it will behave as a pipe with one end closed and the other end open. Such a system produces odd harmonics."
    },
    {
        "instruction": "A force applied on a subject causes 650 m displacement in the direction of the force. If work done is equal to 9872 J, then what is the value of force?",
        "input": "F = W / s",
        "output": "Using the formula: F = W / s, the final answer is: {'answer': '15.2 N', 'explanation': 'To calculate the force, we use the formula F = W / s, where F is the force, W is the work done (9872 J), and s is the displacement (650 m).'}"
    },
    {
        "instruction": "A wire of material-1 of cross-sectional area 3 x 10^(-6) m^2 stretches by the same amount as a wire of material-2 of cross-sectional area 12 x 10^(-6) m^2 under a given load. What is the ratio of the Young\u2019s modulus of material-1 to that of material-2, assuming the ratio of their lengths is 111/177?",
        "input": "ratio = (l1 * A2) / (l2 * A1)",
        "output": "The ratio of the Young's modulus of material-1 to that of material-2 is approximately 2.51. To calculate the ratio, we use the formula:\n\nratio = (l1 * A2) / (l2 * A1)"
    },
    {
        "instruction": "The piston in the cylinder head of a locomotive has a stroke (2 times the amplitude) of 41 m. If the piston moves with SHM with an angular frequency of 515 rev/min, what its amplitude, maximum speed?\n",
        "input": "amp2 = amp/ratio, v = (freq*amp2)/60",
        "output": "amp2 = amp/ratio, v = (freq*amp2)/60  this is the final answer: amplitude is 2.05e+01 m, its maximum speed is 1.76e+02 ms-1\n"
    },
    {
        "instruction": "What is the gravitational field at a point P at a distance of 268 m from a mass of 425 kg?",
        "input": "Gravitational Field (g) = cal3(425, 268) N/kg",
        "output": "The gravitational field at a point P at a distance of 268 m from a mass of 425 kg is given by the formula g = (-G * m) / (r^2), where G is the gravitational constant, m is the mass, and r is the distance. Plugging in the values, we get g = -3.95e-13 N/kg."
    },
    {
        "instruction": "A concave mirror produces 67 times magnified virtual image of an object placed at 4.69 cm in front of it. At what distance is the image formed from the mirror?",
        "input": "Formula: v = u / n",
        "output": "To find the distance at which the image is formed from the mirror, we use the formula v = u / n, where v is the distance of the image from the mirror, u is the distance of the object from the mirror, and n is the magnification factor. By substituting the given values into the formula, we can solve for v. In this case, the image is formed at a distance of 0.1 cm from the mirror., this is the final The image is formed at a distance of 0.1 cm from the mirror."
    },
    {
        "instruction": "What is the largest average velocity of blood flow in an artery of radius 1434 micrometer and length 138 mm if flow must remain laminar? What is the corresponding flow rate?",
        "input": "(2000 * 2.084) / (1.06 * 2 * 1434)",
        "output": "The largest average velocity of blood flow is 1.37 m/s. The corresponding flow rate is 8.86e-06 m^3/s."
    },
    {
        "instruction": "In a chamber, a uniform magnetic field of 0.012 T is maintained. An electron is shot into the field with a speed of 85000000 m/s, making an angle of 21 degrees with the field. Determine the frequency of the revolution of the electron.",
        "input": "Frequency of revolution = (b * e) / (2 * pi * m)",
        "output": "To calculate the frequency of revolution, we use the following formula:\n\nFrequency of revolution = (b * e) / (2 * pi * m)\n\nSubstituting the given values:\n- b = 0.012 T\n- e = 1.6000000000000002e-19 C\n- m = 9.1e-31 kg\n\nAfter evaluating the formula, we find that the frequency of revolution is approximately 3.36e+08 sec^-1."
    },
    {
        "instruction": "A 28 kg mass, fastened to the end of a steel wire of initial length 20 m, is whirled in a vertical circle with an angular velocity of 7 rev/s at the bottom of the circle. The cross-sectional area of the wire is 18 mm^2. Calculate the elongation of the wire when the mass is at the lowest point of its path.",
        "input": "elongation = (force * length) / (A * 10^(-6) * Y_steel)",
        "output": "To calculate the elongation, we use the formula:\n\nelongation = (force * length) / (A * 10^(-6) * Y_steel)\n = (28 kg * (9.8 + 20 m * \u03c0^2 * 7^2) * 20 m) / (18 mm^2 * 10^(-6) m^2 * (2 * 10^11 N/m^2))\n = 150.6 cm."
    },
    {
        "instruction": "A helicopter of mass 1191 kg rises with a vertical acceleration of 4 m/s^2. The crew and the passengers weigh 380 kg. Give the magnitude and direction of",
        "input": "action of the rotor of the helicopter on surrounding air",
        "output": "21994 newton, vertically downwards\n\nThe action of the rotor of the helicopter on surrounding air can be calculated based on the given mass (1191 kg), weight of crew and passengers (380 kg), and acceleration (4 m/s^2)."
    },
    {
        "instruction": "A trolley of mass 42 kg moves with a uniform speed of 3 m/s on a frictionless track. A child of mass 36 kg runs on the trolley from one end to the other (3 m away) with a speed of 3 m/s relative to the trolley in a direction opposite to the trolley\u2019s motion, and jumps out of the trolley. What is the final speed of the trolley?",
        "input": "v_final = (m2 * v2) / (m1 + m2) + v1",
        "output": "Using the formula: v_final = (m2 * v2) / (m1 + m2) + v1, the final answer is: {'answer': '4.4 m/s', 'explanation': 'To find the final speed of the trolley, we use the principle of conservation of momentum. The momentum of the trolley and the child before the child jumps off is equal to the momentum of the trolley after the child jumps off. Using this principle, we can calculate the final speed of the trolley as 4.4 m/s m/s.'}"
    },
    {
        "instruction": "A transverse harmonic wave on a string is described by y(x, t) = 21 sin (92 t + 0.049 x + \u03c0/9) where x and y are in cm and t in s. The positive direction of x is from left to right, then what is value of amplitude?\n",
        "input": "distance = 2*pi/k",
        "output": "0.21 m\nThe amplitude represents the maximum displacement of the wave from its equilibrium position. In this case, the amplitude is 21 units, indicating that the wave oscillates between a maximum positive displacement of 21 units and a maximum negative displacement of 21 units from the equilibrium position."
    },
    {
        "instruction": "About 60 percent of the power of a 232 W light bulb is converted to visible radiation. What is the average intensity of the visible radiation at a distance of 140 m from the bulb?\n",
        "input": "Average Intensity = (Percentage Power / Total Power) / (4 * pi * distance^2)",
        "output": "1.05e-04 watt/m2\n\n\nThe average intensity of the visible radiation at a distance 'd' from the bulb can be calculated using the formula Average Intensity = (Percentage Power / Total Power) / (4 * pi * distance^2), where Percentage Power is the percentage of power converted to visible radiation, Total Power is the total power of the light bulb, and 'd' is the distance from the bulb."
    },
    {
        "instruction": "The far point of a myopic person is 15892 mm in front of the eye. What is the nature and power of the lens required to correct the problem.\n",
        "input": "1/f = 1/v-1/u",
        "output": "the remedial lens should make the objects at infinity appear at far point, hence u = infinity, v = far point of defected eye, from P=1/f, 1/f=1/v-1/u, we get P=1/v-1/u, P=1/v-0=1/v, implies P = 0.06 diatrope, type of lens required is concave.\n"
    },
    {
        "instruction": "A solid cylinder of mass 936 kg has a radius of 61 m and length of 53 m. What is the moment of inertia with respect to its diameter?",
        "input": "Moment of Inertia = (Constant1) * mass * length^2 + (Constant2) * mass * radius^2",
        "output": "The moment of inertia with respect to its end is approximately 219102.0 kgm^2.\n\nMoment of Inertia = (Constant1) * mass * length^2 + (Constant2) * mass * radius^2\n\nConstant1 = 0.08333333333333333\nConstant2 = 0.5\nmass = 936 kg\nlength = 53 m\nradius = 61 m"
    },
    {
        "instruction": "A wheel reaches an angular position of 965 rad when applied with a constant angular acceleration of 29 rad/s\u00b2 for 6 seconds. What is its initial angular velocity?",
        "input": "initial_angular_velocity = (angular_position - (0.5 * angular_acceleration * time^2)) / time",
        "output": "To calculate the initial angular velocity, we use the following formula:\n\ninitial_angular_velocity = (angular_position - (0.5 * angular_acceleration * time^2)) / time\n\nSubstituting the given values into the formula, we find that the initial angular velocity is approximately 73.8 rad/s."
    },
    {
        "instruction": "Two trains A and B of length 57 m each are moving on two parallel tracks with a uniform speed of 687 m/s in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by 4 m/s\u00b2. If after 29 s, the guard of B just brushes past the driver of A, what was the original distance between them?",
        "input": "separation distance = (1 / 2) * acceleration * (time ** 2)",
        "output": "acceleration of B is 4 m/s\u00b2, time taken by B to cover the separation distance is 29 s, length of each train is 57 m, speed of each train is 687 m/sThe original distance between the two trains is 1568.0 m.\n\nseparation distance = (1 / 2) * acceleration * (time ** 2)\n\nThe separation distance between the two trains is the distance covered by the guard of B in the time interval of 29 s. The guard of B covers this distance in the time interval of 29 s with an acceleration of 4 m/s\u00b2. The original distance between the two trains is the separation distance minus the sum of the lengths of the two trains."
    },
    {
        "instruction": "An object of mass 2773 g stands on a weighing machine in a lift, which is moving upwards with a uniform speed of 175 cm/s.",
        "input": "Scale Reading = m * 10 - v",
        "output": "27555\nTo calculate the scale reading, we use the formula Scale Reading = mass * 10 - velocity, where the mass is 2773 g and the velocity is 175 cm/s."
    },
    {
        "instruction": "What is the electric field at a point P on the surface of the spherical shell of radius 143 m and having 1.90e-07 C charge distributed uniformly on it?",
        "input": "Electric Field (E) = cal3(1.90e-07, 143) N/C",
        "output": "8.36e-02 newton/coulomb\nThe electric field on the surface of a uniformly charged spherical shell is given by the formula E = k * Q / (R^2), where k is the Coulomb's constant, Q is the charge on the shell, and R is the radius of the shell. Plugging in the values, we get E = 8.36e-02 N/C."
    },
    {
        "instruction": "Find the value of g using simple pendulum, the following observations were made: length of thread l = 269 +/- 1 cm, time period of oscillation T = 0.92 +/- 0.07 s, then value of g in error limits is?\n",
        "input": "g = (4\u03c0\u00b2l) / T\u00b2",
        "output": "12534.18+/-1953.97\nTo find the value of acceleration due to gravity (g) using a simple pendulum, we can use the formula: g = (4\u03c0\u00b2l) / T\u00b2, where l is the length of the pendulum and T is the time period of oscillation. In this case, the length of the pendulum is 269 cm, and the time period of oscillation is 0.92 s. The error in the length measurement is 1 cm, and the error in the time period measurement is 0.07 s. To determine the error in the calculated value of g, we can use error propagation. The formula for calculating the maximum error in a function involving measured quantities is: Max Error = |dg/dx| * \u0394x, where Max Error is the maximum error, dg/dx is the derivative of the function with respect to the measured quantity (length or time period), and \u0394x is the error in the measured quantity. Taking the derivatives of the g formula with respect to length and time period, we have: dg/dl = (4\u03c0\u00b2) / T\u00b2, dg/dT = -(8\u03c0\u00b2l) / T\u00b3. Substituting the given values into the error propagation formula, we can calculate the maximum error in the value of g: Max Error = |(4\u03c0\u00b2 / T_val\u00b2) * l_error| + |(-(8\u03c0\u00b2l_val) / T_val\u00b3) * t_error. Now, we can substitute the given values to calculate the value of g and its maximum error within the error limits of length and time period."
    },
    {
        "instruction": "A convex lens produces a virtual image at a distance of 154 cm from it of a real object having a height of 73 cm and placed 71 cm in front of it. What is the height of the image?",
        "input": "Formula: hi = (v * ho) / u",
        "output": "To find the height of the image, we use the formula hi = (v * ho) / u, where hi is the height of the image, ho is the height of the object, u is the distance of the object from the lens, and v is the distance of the image from the lens. By substituting the given values into the formula, we can calculate hi. In this case, the height of the image is 158.3 cm., this is the final The height of the image is 158.3 cm."
    },
    {
        "instruction": "A body is dropped from a height of 6855 m with an initial velocity of 14 m/s. With what velocity will it strike the ground?",
        "input": "height (h) = 6855 m, initial velocity (u) = 14 m/s",
        "output": "final velocity (v) = \u221a(initial velocity (u)\u00b2 + 2 * acceleration (g) * height (h))\nv = \u221a(14\u00b2 + 2 * 9.8 * 6855)\nv = \u221a(196 + 134358.0)\nv = \u221a134554.0\nv = \u221a366.8\nv = 366.8"
    },
    {
        "instruction": "A person needs a lens of power -38014 dioptres for correcting his distant vision. What is the focal length of the lens required for correcting distant vision?\n",
        "input": "Power = 1/focal length (f)",
        "output": "we know that power(P)=1/f, hence f=1/P, f(in mm)=1000/P, hence f=0.03 mm\n"
    },
    {
        "instruction": "A bullet of mass 70 g and speed 1193 m/s is fired into a door and gets embedded at the center of the door. The door is 31 m wide and weighs 16 kg. It is hinged at one end and rotates about a vertical axis. Find the angular speed of the door just after the bullet embeds into it.",
        "input": "Angular Speed = (m1 * v1 * l) / (1000 * 2 * I)",
        "output": "To calculate the angular speed of the door, we use the following formula:\n\nAngular Speed = (m1 * v1 * l) / (1000 * 2 * I)\n\nWhere,\n- m1 = Mass of the bullet\n- v1 = Speed of the bullet\n- l = Width of the door\n- I = Moment of inertia of the door\n\nThe moment of inertia of the door can be calculated as I = (m2 * l\u00b2) / 3, where m2 is the mass of the door.\n\nSubstituting the given values into the formula, we find that the angular speed of the door is approximately 0.3 rad/s."
    },
    {
        "instruction": "Two circular coils X and Y of radii 33 cm and 12 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil A has 5 turns and carries a current of 10 A, Coil B has 4 turns and carries a current of 24 A. The sense of current in X is anti-clockwise direction and in Y is clockwise direction. From an observer looking at the coils facing west, give the magnitude and direction of the net magnetic field due to the coils at the center.",
        "input": "Net magnetic field = |b1 - b2|",
        "output": "To calculate the net magnetic field, we use the following formula:\n\nNet magnetic field = |b1 - b2|\n\nWhere,\n- b1 = Magnetic field due to coil X\n- b2 = Magnetic field due to coil Y\n\nWe calculate the magnetic field for each coil using the formula:\n- Magnetic field due to coil X = (mu * n1 * i1) / (2 * r1)\n- Magnetic field due to coil Y = (mu * n2 * i2) / (2 * r2)\n\nSubstituting the given values and evaluating the formula, we find that the magnitude of the net magnetic field is approximately 4.07e-04 tesla and towards west."
    },
    {
        "instruction": "What is the electric field at a point P at a distance of 429 m from the center of the uniform solid sphere of radius 499 m and having -7.10e-07 C charge distributed uniformly.",
        "input": "Electric Field (E) = cal4(-7.10e-07, 429, 499) N/C",
        "output": "-2.21e-02 newton/coulomb\nThe electric field inside a uniformly charged solid sphere is given by the formula E = k * Q * r / (R^3), where k is the Coulomb's constant, Q is the charge on the sphere, r is the distance from the center, and R is the radius of the sphere. Plugging in the values, we get E = -2.21e-02 N/C."
    },
    {
        "instruction": "Assume an unknown planet of orbital period 1802 days is rotating around the sun with an orbit of radius 930 * 10^8 m. What is the ratio of the mass of the sun to the mass of the unknown planet?",
        "input": "Mass Ratio = ((R_earth^3) * (T_planet^2)) / ((R_planet^3) * (T_earth^2)) = ((149.6 * 10^8)^3 * (1802^2)) / ((930 * 10^8)^3 * (365.25^2))",
        "output": "The ratio of the mass of the sun to the mass of the unknown planet is approximately 0.1."
    },
    {
        "instruction": "How much time will a car travelling with a constant velocity of 438 m/s take to travel a distance of 8638 m?",
        "input": "s = 8638 m, v = 438 m/s",
        "output": "The car will take 19.7 s to travel the distance."
    },
    {
        "instruction": "A hoop of mass 3069 kg has a radius of 47 m. What is the moment of inertia with respect to its diameter?",
        "input": "Moment of Inertia = (Constant) * mass * radius^2",
        "output": "The moment of inertia with respect to its diameter is approximately 3389710.5 kgm^2.\n\nMoment of Inertia = (Constant) * mass * radius^2\n\nConstant = 0.5\nmass = 3069 kg\nradius = 47 m"
    },
    {
        "instruction": "A solid sphere of mass 38 kg rotates about its axis with angular speed 31 rad/s. The radius of the sphere is 34 m. What is the magnitude of angular momentum of the sphere about its axis?",
        "input": "Angular Momentum = c * m * r\u00b2 * w",
        "output": "To calculate the magnitude of the angular momentum, we use the following formula:\n\nAngular Momentum = c * m * r\u00b2 * w\n\nWhere,\n- c = Constant for the object\n- m = Mass of the object\n- r = Radius or length of the object\n- w = Angular speed of the object\n\nThe value of the constant (c) depends on the type of object being considered:\n- For a solid cylinder: c = 1/2\n- For a solid sphere: c = 2/5\n- For a hollow sphere: c = 2/3\n- For a rod: c = 1/3\n\nSubstituting the given values into the formula, we find that the magnitude of the angular momentum is approximately 544707.2 kg\u00b7m\u00b2."
    },
    {
        "instruction": "A copper wire has a cross-sectional area of 20 m\u00b2 and length of 27 m. What is the resistivity of this wire that makes its resistance 100 ohm?",
        "input": "R = 100 ohm, A = 20 m\u00b2, l = 27 m",
        "output": "The resistivity of the wire required to achieve a resistance of 100 ohm is 74.1 ohm-m. It is calculated by dividing the product of resistance and area (2000) by the length."
    },
    {
        "instruction": "A child stands at the centre of a turntable with his arms outstretched. The turntable is rotating with an angular speed of 97 rad/s. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to 97/172 times the initial value?",
        "input": "Angular Speed = (n2 * w) / n1\nKinetic Energy Ratio = (n2^3) / (n1^3)",
        "output": "To calculate the angular speed and kinetic energy ratio, we use the following formulas:\n\nAngular Speed = (n2 * w) / n1\nKinetic Energy Ratio = (n2^3) / (n1^3)\n\nWhere,\n- n1 = Initial moment of inertia\n- n2 = Reduced moment of inertia\n- w = Initial angular speed\n\nSubstituting the given values into the formulas, we find that the angular speed of the child is approximately 172.0 rad/s rad/s."
    },
    {
        "instruction": "A liquid has an angle of contact equal to 15 degrees with soda-lime glass. A narrow tube of radius 3 mm made of this glass is dipped in a trough containing liquid. By what amount does the liquid dip down in the tube relative to the liquid surface outside? Surface tension of liquid is 0.16 Nm-2. Density of liquid = 19 x 10^3 kgm-3.",
        "input": "(2 * st * cos(angle * pi / 180)) / (r * density * 9.8)",
        "output": "The liquid in the narrow tube dips down by an amount given by (2 * st * cos(angle * pi / 180)) / (r * density * 9.8). Substituting the given values, we have (2 * 0.16 * cos(15 * 3.141592653589793 / 180)) / (3 * 19 * 10^3 * 9.8) = 5.53e-04 m."
    },
    {
        "instruction": "Two long and parallel straight wires A and B carrying currents of 26 A and 42 A in the opposite direction are separated by a distance 43 cm. Estimate the force and its nature on the 16 cm section of wire A. (mu = 4 x pi x 10^(-7) TmA^-1)",
        "input": "Force = (mu * i1 * i2 * l) / (2 * pi * r)",
        "output": "To calculate the force and its nature, we use the following formula:\n\nForce = (mu * i1 * i2 * l) / (2 * pi * r)\n\nSubstituting the given values:\n- mu = 4 * pi * 10^(-7) TmA^-1\n- i1 = 26 A\n- i2 = 42 A\n- r = 43 cm\n- l = 16 cm\n\nAfter evaluating the formula, we find that the force on the 16 cm section of wire is approximately 8.13e-05 newtons and repulsive."
    },
    {
        "instruction": "A hollow sphere of mass 139 kg rotates about its axis with angular speed 29 rad/s. The radius of the sphere is 6 m. What is the magnitude of angular momentum of the sphere about its axis?",
        "input": "Angular Momentum = c * m * r\u00b2 * w",
        "output": "To calculate the magnitude of the angular momentum, we use the following formula:\n\nAngular Momentum = c * m * r\u00b2 * w\n\nWhere,\n- c = Constant for the object\n- m = Mass of the object\n- r = Radius or length of the object\n- w = Angular speed of the object\n\nThe value of the constant (c) depends on the type of object being considered:\n- For a solid cylinder: c = 1/2\n- For a solid sphere: c = 2/5\n- For a hollow sphere: c = 2/3\n- For a rod: c = 1/3\n\nSubstituting the given values into the formula, we find that the magnitude of the angular momentum is approximately 96744.0 kg\u00b7m\u00b2."
    },
    {
        "instruction": "What is the side of a cube of volume 1398.453 cm3 (in m).\n",
        "input": "Volume = side^3",
        "output": "11182767\nCube of the side is it's volume."
    },
    {
        "instruction": "A toroid has a core of inner radius 70 cm and outer radius 107 cm, around which 250 turns of a wire are wound. If the current in the wire is 33 A, what is the magnetic field inside the core of the solenoid.",
        "input": "Magnetic field = (mu * n * i) / l",
        "output": "To calculate the magnetic field inside the toroid, we use the following formula:\n\nMagnetic field = (mu * n * i) / l\n\nWhere,\n- n = Number of turns of the wire\n- i = Current in the wire\n- l = Length of the wire\n\nWe calculate the length of the wire using the formula:\n- Length of the wire = (r1 + r2) * pi\n\nSubstituting the given values and evaluating the formula, we find that the magnetic field inside the core of the toroid is approximately 1.86e-03 tesla."
    },
    {
        "instruction": "A refrigerator is to maintain eatables kept inside at -53 degree C, if room temperature is 78 degree C. Calculate the coefficient of performance.\n",
        "input": "Coefficient of performance = T2/T1-T2",
        "output": "1.7\nThis formula is only applicable if the refrigerator is based on the Carnot Cycle."
    },
    {
        "instruction": "Two point charges q1 = 36 x 10^(-6)C and q2 = 36 x 10^(-6)C are located 91 cm apart in vacuum. What is the electric field at the midpoint O of the line joining two charges?\n",
        "input": "Electric field = (q1 - q2) / (4 * pi * epsilon * r^2)",
        "output": "To calculate the electric field at the midpoint O, we use the formula:\nElectric field = (q1 - q2) / (4 * pi * epsilon * r^2)\nGiven q1 = 36 x 10^(-6)C, q2 = 36 x 10^(-6)C, and r = 91 cm,\nElectric field = 0.00e+00 newton/coulomb\n"
    },
    {
        "instruction": "A charged 1457 muF capacitor is connected to 694 mH inductor. What is the angular frequency of free oscillations of the circuit?\n",
        "input": "Angular frequency = 1 / sqrt(L * C * 0.001 * 0.000001)",
        "output": "31.4 s-1\n"
    },
    {
        "instruction": "A closely wounded solenoid 678 cm long has 9 layers of windings of 250 turns each. The diameter of the solenoid is d cm. If the current carried is 28 A, estimate the magnitude of the magnetic field inside the solenoid near its center.",
        "input": "B = (mu * n * i) / l",
        "output": "To estimate the magnitude of the magnetic field inside the solenoid near its center, we use the following formula:\n\nB = (mu * n * i) / l\n\nWhere,\n- B = Magnetic field inside the solenoid near its center\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- n = Number of turns per layer\n- i = Current flowing through the solenoid\n- l = Length of the solenoid\n\nSubstituting the given values into the formula, we find that the magnitude of the magnetic field inside the solenoid near its center is approximately 1.30e-03 tesla."
    },
    {
        "instruction": "Find the radius of curvature of a convex mirror whose focal length is 4224.91 cm.",
        "input": "Formula: R = 2 * f",
        "output": "To find the radius of curvature of a convex mirror, we use the formula R = 2 * f, where R is the radius of curvature and f is the focal length. By substituting the given value of f into the formula, we can solve for R. In this case, the radius of curvature is 8449.8 cm., this is the final 8449.8"
    },
    {
        "instruction": "A long straight wire in the horizontal plane carries a current of of 285 A in east to west direction. What is the magnitude and direction of the magnetic field B at a point 1437 cm south of the wire. (mu = 4 x pi x 10-7 TmA-1)\n",
        "input": "B = (mu * i) / (2 * pi * r)",
        "output": "To calculate the magnitude and direction of the magnetic field B, we use the following formula:\n\nB = (mu * i) / (2 * pi * r)\n\nWhere,\n- B = Magnetic field\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- i = Current flowing through the wire\n- r = Distance from the wire\n\nSubstituting the given values into the formula, we find that the magnitude and direction of the magnetic field B is approximately 4.0e-06 tesla vertically upwards\n."
    },
    {
        "instruction": "A man can swim with a speed of 2 m/s in still water. How long does he take to cross a river 66 km wide if the river flows steadily at 190 m/s and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank, and what is the angle of deviation of his path from normal?",
        "input": "v1 = 2 m/s, v2 = 190 m/s, s = 66 km",
        "output": "The time taken is 33000.0 seconds. The distance down the river is 66 km. The angle of deviation is 89 degrees."
    },
    {
        "instruction": "What is the velocity of an object of mass 876 kg having kinetic energy of 498296 J?",
        "input": "v = sqrt((2 * KE) / m)",
        "output": "To calculate the velocity, we use the formula v = sqrt((2 * KE) / m), where v is the velocity, KE is the kinetic energy (498296 J), and m is the mass (876 kg)., this is the final answer 33.7"
    },
    {
        "instruction": "In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are 73 ms-1 and 38 ms-1. What is the lift on the wing if its area is 3000 cm2?",
        "input": "0.5 * 1.3 * (73**2 - 38**2) * (3000 / 10000)",
        "output": "The lift on the wing is 757.5749999999999 newton."
    },
    {
        "instruction": "Suppose we employ a system of units in which the unit of mass equals 34 kg, the unit of length equals 11 m, the unit of time is 13 s, if the value of x pascal is equal to 1042 units in new system, find x\n",
        "input": "x Pa = (Force N) / (Area m\u00b2) = [(m kg) * (l m) / (t\u00b2 s\u00b2)] / [(l m)\u00b2]",
        "output": "19.06\nTo find the value of x pascals in the given system of units, we need to consider the relationships between the units of mass (kg), length (m), time (s), and pressure (Pascal). In the new system of units, we have: 1 unit of mass = 19.06\n kg, 1 unit of length = 11 m, 1 unit of time = 13 s. To find the value of x pascals, we need to determine the conversion factors between the new system and the standard SI units. The pressure (Pascal) can be expressed as: x Pa = (Force N) / (Area m\u00b2) = [(m kg) * (l m) / (t\u00b2 s\u00b2)] / [(l m)\u00b2] = (m * 19.06\n kg) / (t\u00b2 * 13 s\u00b2). Substituting the given values into this equation, we have: x Pa = (m * 19.06\n kg) / (t\u00b2 * 13 s\u00b2). Simplifying this expression will give us the value of x in pascals."
    },
    {
        "instruction": "An image is formed by a convex lens of focal length 334 cm at a distance of 1310 cm behind it. Find at what distance object is placed in front of lens.",
        "input": "Formula: 1/f = 1/v - 1/u for convex lens.",
        "output": "To find the distance of the object from the lens, we use the formula for convex lenses: 1/f = 1/v - 1/u, where f is the focal length ofthe lens, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 448.3 cm from the lens., this is the final The object is placed at 448.3 cm in front of the lens."
    },
    {
        "instruction": "If a force of 1i + -7j + -5k N acts on a body and displaces it 19 m in the direction of x, 2 m in the direction of y, and 39 m in the direction of z, then what is the work done by the force on the body?",
        "input": "Work = (x * sx) + (y * sy) + (z * sz)",
        "output": "To calculate the work done, we use the formula Work = (x * sx) + (y * sy) + (z * sz), where x, y, and z are the components of the force (in N) along the x, y, and z directions, respectively, and sx, sy, and sz are the displacements (in m) in the corresponding directions., this is the final answer -190"
    },
    {
        "instruction": "Two spheres q1 of charge -131 x 10^(-6)C, q2 of charge -116 x 10^(-6)C are placed at a distance 8 cm. If an uncharged sphere C first comes in contact with A, then with B and placed at 8 cm from both of them, then what is the final force between A and C?\n",
        "input": "Final force between A and C = k * qa * qb / d^2",
        "output": "The final force between spheres A and C can be calculated using the formula F = k * qa * qb / d^2, where k is the electrostatic constant, qa and qb are the charges on A and C respectively, and d is the distance between them. Therefore, the final force between A and C is 8.36e+03 newton\n"
    },
    {
        "instruction": "Find the focal length of a concave mirror whose radius of curvature is 9349.34 cm.",
        "input": "Formula: f = R/2",
        "output": "To find the focal length of a concave mirror, we use the formula f = R/2, where f is the focal length and R is the radius of curvature. By substituting the given value of R into the formula, we can solve for f. In this case, the focal length is 4674.7 cm., this is the final 4674.7"
    },
    {
        "instruction": "A copper block of mass 2454 g is heated in a furnace to a temperature of 524 degree C and then placed on a large ice block. What is the maximum amount of ice that can melt? Specific heat of copper is 0.39 Jg-1\u00b0C-1. Heat of fusion of water = 335 Jg-1.",
        "input": "Maximum amount of ice melted = (mass of block * temperature change * specific heat) / heat of fusion of water",
        "output": "To calculate the maximum amount of ice melted, we use the following formula:\n\nMaximum amount of ice melted = (mass of block * temperature change * specific heat) / heat of fusion of water\n\nSubstituting the given values into the formula, we find that the maximum amount of ice that can melt is approximately 1497.0 g."
    },
    {
        "instruction": "A transverse harmonic wave on a string is described by y(x, t) = 15 sin (45 t + 0.057 x + \u03c0/7) where x and y are in cm and t in s. The positive direction of x is from left to right, then what is the initial phase at the origin?\n",
        "input": "distance = 2*pi/k",
        "output": "\u03c0/7\nTo determine the initial phase, we look at the phase term in the equation, which is \"+str(k)+\"x + \u03c0/\"+str(div)+\". At the origin (x=0), the phase term becomes \"+str(\"\u03c0/\"+str(div))+\". Hence, the initial phase at the origin is \"+str(\"\u03c0/\"+str(div))+\" radians or \"+str(\"180/\"+str(div))+\" degrees."
    },
    {
        "instruction": "What is the velocity of an object of mass 745 kg having kinetic energy of 499043 J?",
        "input": "v = sqrt((2 * KE) / m)",
        "output": "To calculate the velocity, we use the formula v = sqrt((2 * KE) / m), where v is the velocity, KE is the kinetic energy (499043 J), and m is the mass (745 kg)., this is the final answer 36.6"
    },
    {
        "instruction": "A body is dropped from a tower with an initial velocity of 685 m/s and reaches the ground with a velocity of 1241 m/s under gravity. What is the time taken by the body to reach the ground?",
        "input": "time = (velocity - initial_velocity) / acceleration",
        "output": "The time taken by the body to reach the ground is 56.7 s."
    },
    {
        "instruction": "A circular disk of radius 206 m weighs 92 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 29 m/s. How much work has to be done to stop it?\n",
        "input": "0.5*(0.5+1)*m*v*v",
        "output": "58029.0 joules\n"
    },
    {
        "instruction": "A train, standing in a station-yard, blows a whistle of frequency 847 Hz in still air. The wind starts blowing in the direction from the yard to the station with a speed of 47 ms-1. What is the speed of sound for an observer standing on the station\u2019s platform? Compare it with situation when the air is still and the observer of mass 66 kg runs towards the yard at a speed of 47 ms-1?\n",
        "input": "Apparent frequency = (speed of sound in air/speed of sound in air - speed of train)*original frequency",
        "output": "case-1(wind) : 387 ms-1, case-2(observer) : 340 ms-1\nTo calculate the frequency heard by an observer standing on the station's platform when the wind is blowing, we need to consider the Doppler effect due to the relative motion between the source of sound and the observer. Given that the train blows a whistle of frequency 847 Hz in still air and the wind is blowing in the direction from the yard to the station with a speed of 47 m/s, we can determine the observed frequency for the platform observer.The formula to calculate the observed frequency is: f' = f * (v_sound + v_wind) / (v_sound), where f' is the observed frequency, f is the emitted frequency, v_sound is the speed of sound in still air, and v_wind is the velocity of the wind."
    },
    {
        "instruction": "Calculate root average velocity of a gas molecule having molar mass of 17 g/mol at 1227 degree C. (R = 8.31 J/molK)",
        "input": "math.sqrt((8 * r * t1 * 1000) / (math.pi * m))",
        "output": "1366.4436849472472 m/s\n The formula used is: math.sqrt((8 * r * t1 * 1000) / (math.pi * m))"
    },
    {
        "instruction": "A convex lens produces 90 times magnified real image of an object at a distance of 2246 cm from the lens. At what distance is the object placed in front of the lens?",
        "input": "Formula: u = v / n",
        "output": "To find the distance at which the object is placed in front of the lens, we use the formula u = v / n, where u is the distance of the object from the lens, v is the distance of the image from the lens, and n is the magnification factor. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 25.0 cm in front of the lens., this is the final The object is placed at a distance of 25.0 cm in front of the lens."
    },
    {
        "instruction": "A convex lens produces a real image at a distance of 7 cm from it of a real object having a height of 48 cm and placed 81 cm in front of it. What is the height of the image?",
        "input": "Formula: hi = (v * ho) / u",
        "output": "To find the height of the image, we use the formula hi = (v * ho) / u, where hi is the height of the image, ho is the height of the object, u is the distance of the object from the lens, and v is the distance of the image from the lens. By substituting the given values into the formula, we can calculate hi. In this case, the height of the image is 4.1 cm., this is the final The height of the image is 4.1 cm."
    },
    {
        "instruction": "A steam engine delivers 520 J of work per minute and services 571 J of heat per minute from its boiler. How much heat is wasted per minute?\n",
        "input": "Efficiency = Work per minute/Heat per minute from its boiler, Heat Wasted = Heat per minute - (Efficiency/100)*Heat per minute",
        "output": "51 joules\nThe efficiency of an engine can be calculated using the formula: Efficiency = (Work output / Heat input) * 100"
    },
    {
        "instruction": "If a physical quantity P=(a^3.0)*(b^-3.0)*(c^-2.5), the percentage errors of measurement in a,b,c are 3%,4%,5% respectively. If the calculated value of P is 29 then what is maximum error possible.\n",
        "input": "Percentage Error in P = |dP/P| * 100",
        "output": "9.71\nTo find the maximum possible error in the calculated value of P, we can use the concept of percentage error propagation. The formula to calculate the percentage error in a quantity calculated from measured quantities is given by: Percentage Error in P = |dP/P| * 100, where dP is the maximum absolute error in P. Since P = (a^3.0)*(b^-3.0)*(c^-2.5), we can differentiate the expression with respect to each measured quantity (a, b, c) to find the maximum absolute error for each term. Then we can substitute the given percentage errors and calculated value of P to find the maximum error. Let's calculate the maximum error using the given information."
    },
    {
        "instruction": "If a car has an initial velocity of 156 m/s and has a constant acceleration of 12 m/s\u00b2, then what is the time taken by the car to attain a velocity of 191 m/s?",
        "input": "time = (final_velocity - initial_velocity) / acceleration",
        "output": "The time taken by the car to attain a velocity of 191 m/s is 2.9 s."
    },
    {
        "instruction": "A meter stick of mass 25 g is balanced on a knife edge at its center. Where will the stick be balanced when a coin of mass 95 g is put at the 6 mark?",
        "input": "Balance Position = ((50 * m) + (m1 * t1)) / (m + m1)",
        "output": "The stick will be balanced at approximately 15.2 cm.\nBalance Position = ((50 * 25) + (95 * 6)) / (25 + 95)"
    },
    {
        "instruction": "A train runs along an unbanked circular track of radius 467 m at a speed of 160 m/s. The mass of the train is 188 kg. What is the angle of banking required to prevent wearing out of the rail?",
        "input": "((atan((v^2) / ((param + 400) * g))) * 180) / pi",
        "output": "80\nTo calculate the angle of banking, we use the formula ((atan((v^2) / ((param + 400) * g))) * 180) / pi, where v is the speed (160 m/s), g is the acceleration due to gravity (10 m/s^2), and param is the radius (467 m) of the circular track."
    },
    {
        "instruction": "A long straight wire in the horizontal plane carries a current of of 344 A in south to north direction. What is the magnitude and direction of the magnetic field B at a point 1966 cm west of the wire. (mu = 4 x pi x 10-7 TmA-1)\n",
        "input": "B = (mu * i) / (2 * pi * r)",
        "output": "To calculate the magnitude and direction of the magnetic field B, we use the following formula:\n\nB = (mu * i) / (2 * pi * r)\n\nWhere,\n- B = Magnetic field\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- i = Current flowing through the wire\n- r = Distance from the wire\n\nSubstituting the given values into the formula, we find that the magnitude and direction of the magnetic field B is approximately 3.5e-06 tesla vertically upwards\n."
    },
    {
        "instruction": "A convex lens produces a real image at a distance of 11 cm from it of a real object having a height of 75 cm and placed 48 cm in front of it. What is the height of the image?",
        "input": "Formula: hi = (v * ho) / u",
        "output": "To find the height of the image, we use the formula hi = (v * ho) / u, where hi is the height of the image, ho is the height of the object, u is the distance of the object from the lens, and v is the distance of the image from the lens. By substituting the given values into the formula, we can calculate hi. In this case, the height of the image is 17.2 cm., this is the final The height of the image is 17.2 cm."
    },
    {
        "instruction": "A polythene is rubbed with wool is found to have a negative charge of 401864 x 10^(-12) C. Estimate the number of electrons transferred (from which to which)?\n",
        "input": "Number of electrons = (charge / elementary charge)",
        "output": "To estimate the number of electrons transferred, we use the formula:\nNumber of electrons = (charge / elementary charge)\nGiven charge = 401864 x 10^(-12) C and elementary charge = 1.6 x 10^(-19) C,\nNumber of electrons = 2.512e+12 electrons transfered from wool to polythene\n"
    },
    {
        "instruction": "In a harbour, wind is blowing at the speed of 3140 m/s and the flag on the mast of a boat anchored in the harbour flutters along the N-E direction. If the boat starts moving at a speed of 260 m/s to the north, what is the direction of the flag on the mast of the boat?",
        "input": "v1 = 3140 m/s, v2 = 260 m/s",
        "output": "41 degrees north of east"
    },
    {
        "instruction": "A rope of negligible mass is wound round a hollow cylinder of mass 90 kg and radius 83 cm. What is the linear acceleration of the hollow cylinder if the rope is pulled with a force of 16 N? Assume that there is no slipping.",
        "input": "Acceleration = Force / (k * mass * radius)",
        "output": "Acceleration = 16 N / (1 * 90 kg * 83 cm)\n\nTo calculate the linear acceleration of the hollow cylinder, we use the following formula:\n\nAcceleration = Force / (k * mass * radius)\n\nSubstituting the values:\n\nForce = 16 N\nk = 1\nMass = 90 kg\nRadius = 83 cm\n\nWe find that the linear acceleration of the hollow cylinder is approximately 0.2 m/s\u00b2."
    },
    {
        "instruction": "A 3m long tube open at one end, with a movable piston at the other end, shows resonance with a fixed frequency source (a turning fork of frequency 1053 Hz) when the tube length is 65 cm or 188 cm. Estimate the speed of sound in air.\n",
        "input": "wavelength = 4*length of tube, speed of sound = frequency*wavelength",
        "output": "2.74e+03 ms-1\nSince the given pipe is attached with a piston at one end, it will behave as a pipe with one end closed and the other end open. Such a system produces odd harmonics."
    },
    {
        "instruction": "In a Youngs double-slit experiment, the slits are seperated by 0.99 mm and the screen is placed 9.8 m away. The distance between the central bright fringe and the 5 bright fringe is measured to be 7 cm. Determine the wavelength of the ligth used for the experiment.\n",
        "input": "Distance between central bright fringe and bright fringe = (wavelength of light*distance from screen)/distance between slits",
        "output": "1.41e-06 m\nIn a Young's double-slit experiment, the wavelength of light can be determined using the formula: \u03bb = (d * sin(\u03b8)) / n, where \u03bb is the wavelength of light, d is the separation between the slits, \u03b8 is the angle of the fringe (in radians), and n is the order of the fringe."
    },
    {
        "instruction": "A body is dropped from a height of 5518 m and reaches the ground with a velocity of 108165 m/s. With what initial velocity was it dropped?",
        "input": "height (h) = 5518 m, final velocity (v) = 108165 m/s",
        "output": "initial velocity (u) = \u221a(final velocity (v)\u00b2 - 2 * acceleration (g) * height (h))\nu = \u221a(108165\u00b2 - 2 * 9.8 * 5518)\nu = \u221a(11699667225 - 108152.8)\nu = \u221a11699559072.2\nu = \u221a108164.5\nu = 108164.5"
    },
    {
        "instruction": "The mass of a particle is 4.65e-29 kg. If its velocity is 1561 m/s, calculate its wavelength.\n",
        "input": "Wavelength = h/mass*velocity",
        "output": "0.02m\nThe momentum (p) of a particle is given by the product of its mass (m) and velocity (v), according to the formula P=M*VThe wavelength (\u03bb) of a particle can be calculated using the de Broglie wavelength equation, which relates the wavelength of a particle to its momentum."
    },
    {
        "instruction": "A series LCR circuit is connected to a variable frequency 230 V source with L = 193 H, C = 182 muF, R = 76 ohm. Determine the impedance of the circuit at the resonating frequency?",
        "input": "Impedance = sqrt(R^2 + (\u03c9L - 1 / (\u03c9C))^2)",
        "output": "76 ohm"
    },
    {
        "instruction": "A concave mirror produces a real image at a distance of 732 cm from it of a real object placed 977 cm in front of it. What is the magnification of the mirror?",
        "input": "Formula: m = v / u",
        "output": "To find the magnification of the mirror, we use the formula m = v / u, where m is the magnification, v is the distance of the real image, and u is the distance of the real object from the mirror. By substituting the given values into the formula, we can solve for m. In this case, the magnification of the mirror is 0.7., this is the final The magnification of the mirror is 0.7."
    },
    {
        "instruction": "In a process, change in internal energy of the system is 626 J. If 7758 J of work is done on the system, what is the amount of heat absorbed by the process ?\n",
        "input": "\u0394U = Q+W",
        "output": "from first law of thermodynamics, du = q + w => q = du - w => q = (626) - (+7758) => q = -7132joule\n"
    },
    {
        "instruction": "If a physical quantity P=(a^0.5)*(b^-0.5)*(c^1.5), the percentage errors of measurement in a,b,c are 3%,4%,3% respectively. If the calculated value of P is 35 then what is maximum error possible.\n",
        "input": "Percentage Error in P = |dP/P| * 100",
        "output": "2.8\nTo find the maximum possible error in the calculated value of P, we can use the concept of percentage error propagation. The formula to calculate the percentage error in a quantity calculated from measured quantities is given by: Percentage Error in P = |dP/P| * 100, where dP is the maximum absolute error in P. Since P = (a^0.5)*(b^-0.5)*(c^1.5), we can differentiate the expression with respect to each measured quantity (a, b, c) to find the maximum absolute error for each term. Then we can substitute the given percentage errors and calculated value of P to find the maximum error. Let's calculate the maximum error using the given information."
    },
    {
        "instruction": "If a gas of 9 moles at 14 pas is isothermally changed to pressure 12 pas at 42 K, then what is the work done.\n",
        "input": "Work Done = n*R*T*ln(P1/P2)",
        "output": "-484.2 joules\nTo calculate the work done during an isothermal expansion of a monoatomic gas, we can use the following equation: Work done = n * R * T * ln(P1/P2), where n is the number of moles of the gas, R is the ideal gas constant (approximately 8.314 J/(mol\u00b7K)), T is the temperature in Kelvin, P1 is the initial pressure, and P2 is the final pressure."
    },
    {
        "instruction": "A long straight wire in the horizontal plane carries a current of of 389 A in south to north direction. What is the magnitude and direction of the magnetic field B at a point 488 cm east of the wire. (mu = 4 x pi x 10-7 TmA-1)\n",
        "input": "B = (mu * i) / (2 * pi * r)",
        "output": "To calculate the magnitude and direction of the magnetic field B, we use the following formula:\n\nB = (mu * i) / (2 * pi * r)\n\nWhere,\n- B = Magnetic field\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- i = Current flowing through the wire\n- r = Distance from the wire\n\nSubstituting the given values into the formula, we find that the magnitude and direction of the magnetic field B is approximately 1.6e-05 tesla vertically downwards\n."
    },
    {
        "instruction": "A transverse harmonic wave on a string is described by y(x, t) = 35 sin (19 t + 0.149 x + \u03c0/9) where x and y are in cm and t in s. The positive direction of x is from left to right, is this a travelling wave or a stationary wave? If it is travelling, what are the speed and direction of its propagation ?\n",
        "input": "speed = frequency*wavelength",
        "output": "it is a travelling wave, it is travelling in -ve x direction with 1.28e+02 ms-1\nFor a traveling wave, the speed of propagation (v) can be determined by the ratio between the angular frequency (\u03c9) and the wave number (k): v = \u03c9 / k. In this case, the angular frequency is \"+str(w)+\" and the wave number is \"+str(k)+\". We can calculate the speed of propagation using these values: v = \"+str(w)+\" / \"+str(k)"
    },
    {
        "instruction": "Obtain the Q-value of a series LCR circuit with L = 150 H, C = 150 muF, R = 166 ohm?\n",
        "input": "Q-value = (1 / R) * sqrt(L / (C * 0.000001))",
        "output": "6.0\n"
    },
    {
        "instruction": "Calculate the frequency of a sound wave whose wavelength is 356 m and speed is 24920 m/s in a given medium ?\n",
        "input": "Wavelength = Speed / Frequency",
        "output": "70 hz\nTo calculate the frequency of a sound wave, we can use the formula: Frequency = Speed / Wavelength. In this case, the speed of the sound wave is 24920 m/s and the wavelength is 356 m. Substituting these values into the formula, we can calculate the frequency: Frequency = 24920 m/s / 356 m"
    },
    {
        "instruction": "What is the focal length of a concave lens of focal length 174 cm in contact with a concave lens of focal length 94 cm? Is the system a converging or a diverging lens? Ignore thickness of the lenses.",
        "input": "Formula: For two lenses in contact, the combined focal length (P) is given by P = (f1 * f2) / (f1 + f2), where f1 and f2 are the focal lengths of the lenses.",
        "output": "This is the answer {answer}, formula used is : {formula}"
    },
    {
        "instruction": "How much should the pressure of 6080 ml of water be changed to compress it by 4.3%, assuming a bulk modulus of elasticity of water to be 2.2 x 10^9 N/m^2?",
        "input": "pressure_change = (bulk_modulus * percent) / 100",
        "output": "The pressure of 6080 ml of water needs to be changed by 9.5e+07 Pa to compress it by 4.3%. The formula to calculate the pressure change is:\n\npressure_change = (bulk_modulus * percent) / 100"
    },
    {
        "instruction": "Suppose we employ a system of units in which the unit of mass equals 35 kg, the unit of length equals 44 m, the unit of time is 81 s, then value of 30 joules in new system\n",
        "input": "30 J = (m kg) * (l m^2) / (t^2 s^2)",
        "output": "2.9\nTo find the value of 30 joules in the given system of units, we need to consider the relationships between the units of mass (kg), length (m), time (s), and energy (Joule). In the new system of units, we have: 1 unit of mass = 2.9\n kg, 1 unit of length = 44 m, 1 unit of time = 81 s. To find the value of 30 joules, we need to determine the conversion factors between the new system and the standard SI units. The energy (Joule) can be expressed as: 30 J = (m kg) * (l m^2) / (t^2 s^2). Substituting the given values into this equation, we have:30 J = (m * 2.9\n kg) * (l * 44 m^2) / (t^2 * 81 s^2). Simplifying this expression will give us the value of 30 joules in the new system of units."
    },
    {
        "instruction": "Two moving coil meters M1 and M2 have the following particulars R1 = 8 ohms, N1 = 7, A1 = 0.0006000000000000001 m2 , B1 = 8 T, K1 = 6 and  R2 = 2 ohms, N2 = 8 , A1 = 0.0002 m2 , B1 = 10 T, K2 = 10. Determine the ratio of current sensitivities of M1 and M2.\n",
        "input": "Ratio of current sensitivity of M1 to M2 is given by, n1 x b1 x a1 x k2 : n2 x b2 x a2 x k1",
        "output": "Ratio of current sensitivity of M1 to M2 is given by, n1 x b1 x a1 x k2 : n2 x b2 x a2 x k1 = 7 x 8 x 0.0006000000000000001 x 10 : 8 x 10 x 0.0002 x 6 = 3.5\n"
    },
    {
        "instruction": "A hoop rolls down two different inclined planes of the same height 10 cm but with angles of inclination of 4 and 78, on which it will reach the ground faster?",
        "input": "time = sqrt((k + 1) * height) / sin(angle)",
        "output": "To compare the times, we use the following formula:\n\ntime = sqrt((k + 1) * height) / sin(angle)\n\nSubstituting the given values into the formula, we find that:\n\nThe second plane takes less time to reach the ground."
    },
    {
        "instruction": "A steel cable with a radius of 23 mm supports a chairlift at a ski area. If the maximum stress is not to exceed 15197 x 10^(6) Nm-2, what is the maximum load the cable can support?",
        "input": "",
        "output": "The maximum load the cable can support is 2.5e+01 newton."
    },
    {
        "instruction": "A large steel wheel is to be fitted onto a shaft of the same material. At 146 degree C, the outer diameter of the shaft is 107 cm and the diameter of the central hole in the wheel is 106.993 cm. The shaft is cooled using 'dry ice'. At what temperature of the shaft does the wheel slip on the shaft? Assume the coefficient of linear expansion of the steel to be constant over the required temperature range \u03b1steel = 1.20 x 10-5K-1.",
        "input": "Required temperature = t1 + ((d2 - d1) / (\u03b1 * d1))",
        "output": "To calculate the required temperature, we use the following formula:\n\nRequired temperature = t1 + ((d2 - d1) / (\u03b1 * d1))\n\nSubstituting the given values into the formula, we find that the temperature is approximately 140.5 degree C."
    },
    {
        "instruction": "A convex mirror produces a real image of height 257 cm of a real object of height 414 cm placed in front of it. What is the magnification of the mirror?",
        "input": "Formula: m = hi / ho = v / u",
        "output": "To find the magnification of the convex mirror, we use the formula m = hi / ho = v / u, where m is the magnification, hi is the height of the image, ho is the height of the object, v is the distance of the image from the mirror, and u is the distance of the object from the mirror. Since the heights are provided instead of distances, the formula still holds. By substituting the given values into the formula, we can calculate the magnification. In this case, the magnification of the mirror is 0.6., this is the final The magnification of the mirror is 0.6."
    },
    {
        "instruction": "Assume an unknown planet of orbital period 890 days is rotating around the sun with an orbit of radius 530 * 10^8 m. What is the ratio of the mass of the sun to the mass of the unknown planet?",
        "input": "Mass Ratio = ((R_earth^3) * (T_planet^2)) / ((R_planet^3) * (T_earth^2)) = ((149.6 * 10^8)^3 * (890^2)) / ((530 * 10^8)^3 * (365.25^2))",
        "output": "The ratio of the mass of the sun to the mass of the unknown planet is approximately 0.1."
    },
    {
        "instruction": "A double convex lens has radii of curvatures 49 cm and 88 cm, and is made of material with a refractive index of 1.57. What is the focal length of the lens?",
        "input": "Formula: f = 1 / ((mu - 1) * ((1 / r1) - (1 / r2)))",
        "output": "To find the focal length of the double convex lens, we use the formula f = 1 / ((mu - 1) * ((1 / r1) - (1 / r2))), where f is the focal length, mu is the refractive index of the lens material, r1 is the radius of curvature of the first surface, and r2 is the radius of curvature of the second surface. By substituting the given values into the formula, we can solve for f. In this case, the focal length of the lens is 55.22 cm., this is the final The focal length of the lens is 55.22 cm."
    },
    {
        "instruction": "A jet airplane ejects its combustion products at the speed of 711 m/s with respect to the jet plane. If the speed of the combustion products with respect to an observer on the ground is 785 m/s, then what is the speed of the plane?",
        "input": "v1 = 711 m/s, v2 = 785 m/s",
        "output": "1496"
    },
    {
        "instruction": "A closely wounded solenoid 274 cm long has 6 layers of windings of 300 turns each. The diameter of the solenoid is d cm. If the current carried is 1 A, estimate the magnitude of the magnetic field inside the solenoid near its center.",
        "input": "B = (mu * n * i) / l",
        "output": "To estimate the magnitude of the magnetic field inside the solenoid near its center, we use the following formula:\n\nB = (mu * n * i) / l\n\nWhere,\n- B = Magnetic field inside the solenoid near its center\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- n = Number of turns per layer\n- i = Current flowing through the solenoid\n- l = Length of the solenoid\n\nSubstituting the given values into the formula, we find that the magnitude of the magnetic field inside the solenoid near its center is approximately 1.38e-04 tesla."
    },
    {
        "instruction": "A concave lens produces a real image at a distance of 16 cm from it of a real object having a height of 21 cm and placed 94 cm in front of it. What is the height of the image?",
        "input": "Formula: hi = (v * ho) / u",
        "output": "To find the height of the image, we use the formula hi = (v * ho) / u, where hi is the height of the image, ho is the height of the object, u is the distance of the object from the lens, and v is the distance of the image from the lens. By substituting the given values into the formula, we can solve for hi. In this case, the height of the image is 3.6 cm., this is the final The height of the image is 3.6 cm."
    },
    {
        "instruction": "Two masses each of mass 91 kg are attached by a spring with K = 163 Nm-1. If a force of 58 N is applied at the free ends of both masses, then what is the time period of oscillation?",
        "input": "Formula: T = 2\u03c0\u221a(m / (2k)), where T is the time period of oscillation, m is the mass of each mass (91 kg), and k is the spring constant (163 Nm-1).",
        "output": "Using this formula: Formula: T = 2\u03c0\u221a(m / (2k)), where T is the time period of oscillation, m is the mass of each mass (91 kg), and k is the spring constant (163 Nm-1)., this is the final answer derived: 3.32e+00 s"
    },
    {
        "instruction": "Find the power of a concave lens whose focal length is 92.17 m.",
        "input": "Formula: P = 1 / f",
        "output": "To find the power of a concave lens, we use the formula P = 1 / f, where P is the power and f is the focal length. By substituting the given value of f into the formula, we can solve for P. In this case, the power is 0.0 diatrope., this is the final 0.0"
    },
    {
        "instruction": "685 A of current flows through a circuit. If the rate of heat generated is 348 W, calculate the potential difference of the battery?",
        "input": "V = P / I",
        "output": "0.5 volt\n\nThe potential difference of the battery can be calculated using the formula: V = P / I, where P is the rate of heat generated and I is the current."
    },
    {
        "instruction": "What is the gravitational field at a point P at a distance of 6 m from the center of the uniform solid sphere of radius 15 m and mass 224 kg?",
        "input": "Gravitational Field (g) = cal2(224, 6, 15) N/kg",
        "output": "The gravitational field at a point P at a distance of 6 m from the center of the uniform solid sphere of radius 15 m and mass 224 kg is given by the formula g = (-G * m * r) / (R^3), where G is the gravitational constant, m is the mass, r is the distance, and R is the radius. Plugging in the values, we get g = -2.66e-11 N/kg."
    },
    {
        "instruction": "A concave lens produces a real image of height 89 cm of a real object having a height of 166 cm and placed 31 cm in front of it. At what distance is the image formed from the lens?",
        "input": "Formula: v = (u * hi) / ho",
        "output": "To find the distance at which the image is formed from the lens, we use the formula v = (u * hi) / ho, where v is the distance of the image from the lens, u is the distance of the object from the lens, hi is the height of the image, and ho is the height of the object. By substituting the given values into the formula, we can solve for v. In this case, the distance at which the image is formed from the lens is 16.6 cm., this is the final The distance at which the image is formed from the lens is 16.6 cm."
    },
    {
        "instruction": "A circular coil of wire consisting of 60 turns, each of radius 35 cm carries a current of 1 A. What is the magnitude of the magnetic field B at a point on the axis which is 95 cm from the center of the coil?",
        "input": "B = (mu * n * i * r^2) / (2 * sqrt((r^2 + x^2)^3))",
        "output": "To calculate the magnetic field B at a point on the axis, which is 95 cm from the center of the coil, we use the following formula:\n\nB = (mu * n * i * r^2) / (2 * sqrt((r^2 + x^2)^3))\n\nWhere,\n- B = Magnetic field at the point on the axis\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- n = Number of turns in the coil\n- i = Current flowing through the coil\n- r = Radius of the coil\n- x = Distance from the center of the coil to the point on the axis\n\nSubstituting the given values into the formula, we find that the magnitude of the magnetic field B is approximately 4.45e-06 tesla."
    },
    {
        "instruction": "Two discs of moments of inertia 54 and 58 about their respective axes, and rotating with angular speed 11 rad/s and 65 rad/s are brought into contact face to face with their axes of rotation coincident. What is the angular speed of the two-disc system?",
        "input": "Angular Speed = ((i1 * w1) + (i2 * w2)) / (i1 + i2)\nLoss in Kinetic Energy = k1 + k2 - k\n\nk1 = 0.5 * i1 * w1^2\nk2 = 0.5 * i2 * w2^2\nk = 0.5 * (i1 + i2) * w^2",
        "output": "To calculate the angular speed and loss in kinetic energy, we use the following formulas:\n\nAngular Speed = ((i1 * w1) + (i2 * w2)) / (i1 + i2)\nLoss in Kinetic Energy = k1 + k2 - k\n\nWhere,\n- i1 = Moment of inertia of the first disc\n- i2 = Moment of inertia of the second disc\n- w1 = Angular speed of the first disc\n- w2 = Angular speed of the second disc\n\nSubstituting the given values into the formulas, we find that the angular speed of the two-disc system is approximately 39.0 rad/s rad/s"
    },
    {
        "instruction": "Toricelli's barometer used mercury. If someone duplicated it using some liquid of density 1790 kg/m3. Determine the height of the liquid column for normal atmospheric pressure (density of material of barometer is 1960 kg/m3).",
        "input": "(1.01 * (10 ** 5)) / (1790 * 9.8)",
        "output": "5.757610306692509"
    },
    {
        "instruction": "Two towers on top of two hills are 44 km apart. The line joining them passes 10 m above a hill halfway between the towers. What is the longest wavelength of radio waves, which can be sent between the two towers without appreciable diffraction effects.\n",
        "input": "Fresnel Distance*Aperture = Wavelength of light^2",
        "output": "2.27e-03 m\nTo determine the longest wavelength of radio waves that can be sent between the two towers without appreciable diffraction effects, we can use the Fresnel diffraction criterion. The Fresnel diffraction criterion states that when the distance (d) between the two towers is much larger than the square of the wavelength (\u03bb), diffraction effects can be neglected.In this case, we want to find the maximum wavelength, so we can rearrange the formula to solve for \u03bb: \u03bb \u2248 sqrt(d * l)"
    },
    {
        "instruction": "Two long and parallel straight wires A and B carrying currents of 35 A and 29 A in the same direction are separated by a distance 38 cm. Estimate the force and its nature on the 3 cm section of wire B. (mu = 4 x pi x 10^(-7) TmA^-1)",
        "input": "Force = (mu * i1 * i2 * l) / (2 * pi * r)",
        "output": "To calculate the force and its nature, we use the following formula:\n\nForce = (mu * i1 * i2 * l) / (2 * pi * r)\n\nSubstituting the given values:\n- mu = 4 * pi * 10^(-7) TmA^-1\n- i1 = 35 A\n- i2 = 29 A\n- r = 38 cm\n- l = 3 cm\n\nAfter evaluating the formula, we find that the force on the 3 cm section of wire is approximately 1.60e-05 newtons and attractive."
    },
    {
        "instruction": "Two point charges q1 = -19 x 10^(-6)C and q2 = 132 x 10^(-6)C are located 172 cm apart in vacuum. What is the force on the test charge of -10 x 10^(-6)C placed at the midpoint of the line joining two charges?\n",
        "input": "Electric field = (q1 - q2) / (4 * pi * epsilon * r^2)\nForce = Electric field * test charge",
        "output": "To calculate the force on the test charge at the midpoint, we use the formula:\nForce = Electric field * test charge\nGiven the electric field as calculated before and the test charge qmid = -10 x 10^(-6)C,\nForce = 1.84e+01 newton\n"
    },
    {
        "instruction": "A capacitor with air between it's parallel plates, each plate has an area of 0.0692 m2 and the distance between the plates is 15 mm, if this capacitor is connected to a 413 V supply and a 15 mm thick mica sheet is inserted between the plates, then what will happen?\n",
        "input": "\n# Formula to calculate the capacitance of a parallel-plate capacitor\ncapacitance = (8.854 * 10**-12 * epsilon_r * A) / d\n\n# Formula to calculate the electric field between the plates of a capacitor\nelectric_field = V / d\n\n# Formula to calculate the capacitance of the capacitor with the mica sheet\ncapacitance_with_mica = (8.854 * 10**-12 * epsilon_r_mica * A) / (2 * d)\n",
        "output": "capacitance becomes 2.45e+02 pico-farad, charge becomes 1.01e-07 coulomb\n\n\nExplanation: The capacitance of a parallel-plate capacitor depends on the area of the plates (A) and the distance between them (d). The formula to calculate the capacitance is C = (8.854 * 10**-12 * epsilon_r * A) / d, where epsilon_r is the relative permittivity of the medium between the plates (air in this case). The electric field between the plates of a capacitor is determined by the potential difference (V) applied across the plates and the distance between them (d). The formula to calculate the electric field is E = V / d. When a mica sheet is inserted between the plates, the distance between the plates is effectively reduced to half (2 * d). The capacitance with the mica sheet can be calculated using the same formula as before, but with the relative permittivity of mica (epsilon_r_mica). To summarize, inserting a mica sheet between the plates of the capacitor will decrease the distance between the plates, resulting in an increased capacitance compared to the air-filled capacitor. The electric field between the plates will remain the same, as it depends on the potential difference and the original distance between the plates."
    },
    {
        "instruction": "The cylindrical tube of a spare pump has a cross-section of 75 cm\u00b2, one end of which has 45 fine holes each of diameter 9 mm. If the liquid flow inside the tube is 6 m/min, what is the speed of ejection of the liquid through the holes?",
        "input": "(75 * (10 ** -4) * (6 / 60)) / (math.pi * 9 ** 2 * 0.25 * (10 ** -6))",
        "output": "The speed of ejection of the liquid through the holes is 1.18e+01 m/s."
    },
    {
        "instruction": "A rod of mass 790 kg rotates about its end with angular speed 15 rad/s. The length of the rod is 6 m. What is the magnitude of angular momentum of the rod about its end?",
        "input": "Angular Momentum = c * m * r\u00b2 * w",
        "output": "To calculate the magnitude of the angular momentum, we use the following formula:\n\nAngular Momentum = c * m * r\u00b2 * w\n\nWhere,\n- c = Constant for the object\n- m = Mass of the object\n- r = Radius or length of the object\n- w = Angular speed of the object\n\nThe value of the constant (c) depends on the type of object being considered:\n- For a solid cylinder: c = 1/2\n- For a solid sphere: c = 2/5\n- For a hollow sphere: c = 2/3\n- For a rod: c = 1/3\n\nSubstituting the given values into the formula, we find that the magnitude of the angular momentum is approximately 142200.0 kg\u00b7m\u00b2."
    },
    {
        "instruction": "A concave mirror produces 52 times magnified real image of an object at a distance of 6259 cm from the mirror. At what distance is the object placed in front of the mirror?",
        "input": "Formula: u = v / n",
        "output": "To find the distance at which the object is placed in front of the mirror, we use the formula u = v / n, where u is the distance of the object from the mirror, v is the distance of the image from the mirror, and n is the magnification factor. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 120.4 cm in front of the mirror., this is the final The object is placed at a distance of 120.4 cm in front of the mirror."
    },
    {
        "instruction": "What is the electric field at a point P at a distance of 416 m from the center of the spherical shell of radius 350 m and having 8.00e-08 C charge distributed uniformly on it?",
        "input": "Electric Field (E) = cal2(8.00e-08, 416, 350) N/C",
        "output": "4.16e-03 newton/coulomb\nThe electric field due to a uniformly charged spherical shell is given by the formula E = k * Q * r / (R^2), where k is the Coulomb's constant, Q is the charge on the shell, r is the distance from the center of the shell, and R is the radius of the shell. Plugging in the values, we get E = 4.16e-03 N/C."
    },
    {
        "instruction": "A satellite orbits the earth at a height of 330 km above the surface. How much energy must be expended to rocket the satellite out of the planet's gravitational influence? Mass of the satellite = 200 kg; mass of the planet = 6e+24 kg; radius of the planet = 6400000.0 m.",
        "input": "(g * m * M) / (2 * (r + h))",
        "output": "The energy required to rocket the satellite out of the planet's gravitational influence is approximately 6.25e+09 joules."
    },
    {
        "instruction": "A bike starting with an initial velocity of 57 m/s travels on a straight road at a constant rate of 3 m/s\u00b2. What is the time taken to travel a distance of 885 m?",
        "input": "initial velocity (u) = 57 m/s, acceleration (a) = 3 m/s\u00b2, distance (s) = 885 m",
        "output": "distance (s) = initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)\u00b2\n885 = 57 * t + 0.5 * 3 * t\u00b2\n885 = 672.6 + 208.86000000000004\n885 = 885\n\n0.5 * 3 * t\u00b2 + 57 * t - 885 = 0\n1.5 * t\u00b2 + 57 * t - 885 = 0\n\nUsing quadratic formula, we get:\n\nt = (-57 \u00b1 \u221a(57\u00b2 - 4 * 1.5 * (-885))) / (2 * 1.5)\nt = (-57 \u00b1 \u221a(3249 - 5310)) / 3\nt = (-57 \u00b1 \u221a(8559)) / 3\nt = (-57 \u00b1 \u221a(8559)) / 3\nt = (-57 \u00b1 \u221a(8559)) / 3\nt = (-57 \u00b1 92.51486367065564) / 3\nt = 11.838287890218547 or -49.838287890218545\nt = 11.8 or 11.8\n\nSince time cannot be negative, t = 11.8"
    },
    {
        "instruction": "Two sitar strings A and B playing the note \u2018Ga\u2019 are slightly out of tune and produce beats of frequency 19 Hz. The tension in the string A is slightly reduced and the beat frequency is found to be 49 Hz. If the original frequency of A is 221 Hz, what is the frequency of B?\n",
        "input": "Beat frequency = |f1+-f2|",
        "output": "240 hertz\nFrequency decreases with a decrease in the tension of a string.\nThis is because frequency is directly proportional to the square root of tension."
    },
    {
        "instruction": "An electron is projected between parallel plates separated by 0.8 cm, having a field of 2260 N/C (up to down), with a speed of 189000 m/s. In what time will the electron strike the upper plate?\n",
        "input": "Time Taken Formula: time_taken = sqrt(2 * d * 0.01 * 9.1 * 10^(-31) * v^2 / (1.6 * 10^(-19) * E))\n",
        "output": "1.20e-03 s\n"
    },
    {
        "instruction": "A rectangular wire loop of sides 21 cm and 1 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 17.8 T directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is 58 cm/s in a direction normal to the two different sides of the loop? For how long does the induced voltage last in each case?\n",
        "input": "EMF = B * l * v",
        "output": "2.17e+00 volt for 3.62e-01 s if the velocity is perpendicular to the 21 cm side, 1.03e-01 volt for 1.72e-02 s if the velocity is perpendicular to the 1 cm side\n\n\nThe electromotive force (EMF) can be calculated using the formula EMF = B * l * v, where B is the magnetic field magnitude, l is the side length of the rectangular wire loop, and v is the velocity of the loop after conversion from cm/s to m/s."
    },
    {
        "instruction": "A tank is filled with water to a height of 37.1 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 18.3 cm. What is the refractive index of water?",
        "input": "Formula: refractive index = height of tank / apparent depth of needle",
        "output": "To calculate the refractive index, we use the formula: refractive index = height of tank / apparent depth of needle. In this case, the height of the tank is 37.1 cm and the apparent depth of the needle is 18.3 cm., this is the final 2.03"
    },
    {
        "instruction": "A circular disk of radius 68 m weighs 53 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 40 m/s. How much work has to be done to stop it?\n",
        "input": "0.5*(0.5+1)*m*v*v",
        "output": "63600.0 joules\n"
    },
    {
        "instruction": "What is the phase of the SHM with equation (-6)*sin(73wt) + (-123)*cos(73wt)? (i.e., if written as Asin(bwt+theta), then what is the value of theta)\n",
        "input": "Equation: (-6)*sin(73wt) + (-123)*cos(73wt)",
        "output": "Using this formula: Equation: (-6)*sin(73wt) + (-123)*cos(73wt), this is the final answer derived: 87 degrees\n"
    },
    {
        "instruction": "Assuming the Earth to be a sphere of uniform mass density, how much would a body weigh 17/63 down to the center of the Earth if it weighed 303 N on the surface?",
        "input": "Weight on the Surface (W) = 303 N, Height Ratio (n/d) = 17/63",
        "output": "The weight of the body 17/63 down to the center of the Earth, assuming a uniform mass density, would be 221.2 newtons."
    },
    {
        "instruction": "If a gas of 8 moles at 40 m3 is isothermally changed to volume 60 m3 at 25 K, then what is the work done.\n",
        "input": "Work Done = n*R*T*ln(V2/V1)",
        "output": "-673.9 joules\nTo calculate the work done during an isothermal expansion of a monoatomic gas, we can use the following equation: Work done = n * R * T * ln(V2/V1), where n is the number of moles of the gas, R is the ideal gas constant (approximately 8.314 J/(mol\u00b7K)), T is the temperature in Kelvin, V1 is the initial volume, and V2 is the final volume."
    },
    {
        "instruction": "A capacitor made of two circular plates of radius 148 cm, and separated by 9 cm. The capacitor is being charged by an external source. The charging current is constant and equal to 182 mA. Calculate the capacitance between the plates?",
        "input": "r = 148 cm, s = 9 cm",
        "output": "6.77e-10 farad\n\nThe capacitance of a capacitor can be calculated using the formula: C = (\u03b5\u03c0r\u00b2) / s, where \u03b5 is the permittivity of free space, r is the radius of the plates, and s is the separation between the plates."
    },
    {
        "instruction": "A steel rod 920 cm long is hinged at its middle. The fundamental frequency of longitudinal vibrations of the rod is given to be 2707 Hz. What is the speed of sound in steel?\n",
        "input": "speed of sound in steel = frequency*wavelength",
        "output": "5.0e+04 ms-1\nThe distance between two successive nodes is wavelength/2."
    },
    {
        "instruction": "8 capacitors each of capacitance 212pF are connected in series. What is the total capacitance of the combination when the system is connected to a 58 V supply?\n",
        "input": "1 / C_total = 1 / C1 + 1 / C2 + 1 / C3 + ... + 1 / Cn\n",
        "output": "2.65e+01 pico-farad\n\nExplanation: 1 / C_total = 1 / 212 + 1 / 212 + 1 / 212 + ... + 1 / 212\n"
    },
    {
        "instruction": "A meter stick is balanced on a knife edge at its center. Where will the stick be balanced when two coins, each of mass 36 g and 83 g respectively, are put at the 41 mark and 80 mark respectively?",
        "input": "Balance Position = ((50 * m) + (m1 * t1) + (m2 * t2)) / (m + m1 + m2)",
        "output": "The stick will be balanced at approximately 61.8 cm.\nBalance Position = ((50 * 64) + (36 * 41) + (83 * 80)) / (64 + 36 + 83)"
    },
    {
        "instruction": "A wheel starting with an initial angular velocity of 38 rad/s accelerates and reaches a final velocity of 107 rad/s when the angular position is 64 rad. What is its angular acceleration?",
        "input": "angular_acceleration = ((final_angular_velocity^2 - initial_angular_velocity^2) / (2 * angular_position))",
        "output": "To calculate the angular acceleration, we use the following formula:\n\nangular_acceleration = ((final_angular_velocity^2 - initial_angular_velocity^2) / (2 * angular_position))\n\nSubstituting the given values into the formula, we find that the angular acceleration is approximately 78.2 rad/s\u00b2."
    },
    {
        "instruction": "A bike starting with an initial velocity of 651 m/s travels on a straight road at a constant rate of 19 m/s\u00b2 for 2 s. How far does the bike travel during this time?",
        "input": "initial velocity (u) = 651 m/s, acceleration (a) = 19 m/s\u00b2, time (t) = 2 s",
        "output": "1340.0 m \n\ndistance (s) = initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)\u00b2\ns = 651 * 2 + 0.5 * 19 * 2\u00b2\ns = 1302 + 38.0\ns = 1340.0"
    },
    {
        "instruction": "A convex mirror produces 95 times diminished real image of an object at a distance of 5 cm from the mirror. At what distance is the object placed in front of the mirror?",
        "input": "Formula: u = v * n",
        "output": "To find the distance at which the object is placed in front of the mirror, we use the formula u = v * n, where u is the distance of the object from the mirror, v is the distance of the image from the mirror, and n is the magnification factor. By substituting the given values into the formula, we can calculate u. In this case, the object is placed at a distance of 475 cm in front of the mirror., this is the final The object is placed at a distance of 475 cm in front of the mirror."
    },
    {
        "instruction": "Two discs of moments of inertia 92 and 3 about their respective axes, and rotating with angular speed 42 rad/s and 78 rad/s are brought into contact face to face with their axes of rotation coincident. What is the loss in kinetic energy of the two-disc system?",
        "input": "Angular Speed = ((i1 * w1) + (i2 * w2)) / (i1 + i2)\nLoss in Kinetic Energy = k1 + k2 - k\n\nk1 = 0.5 * i1 * w1^2\nk2 = 0.5 * i2 * w2^2\nk = 0.5 * (i1 + i2) * w^2",
        "output": "To calculate the angular speed and loss in kinetic energy, we use the following formulas:\n\nAngular Speed = ((i1 * w1) + (i2 * w2)) / (i1 + i2)\nLoss in Kinetic Energy = k1 + k2 - k\n\nWhere,\n- i1 = Moment of inertia of the first disc\n- i2 = Moment of inertia of the second disc\n- w1 = Angular speed of the first disc\n- w2 = Angular speed of the second disc\n\nSubstituting the given values into the formulas, we find that the loss in kinetic energy is approximately 1882.6 joules joules."
    },
    {
        "instruction": "A 21 kW drilling machine is used to drill a bore in a small aluminium block of mass 16 kg. How much is the rise in temperature of the block in 6 minutes, assuming 26 percent of power is used up in heating the machine itself or lost to the surroundings? Specific heat of aluminium = 0.91 J g-1 K-1.",
        "input": "Rise in temperature = (p * P * t) / (m * s)",
        "output": "To calculate the rise in temperature, we use the following formula:\n\nRise in temperature = (p * P * t) / (m * s)\n\nSubstituting the given values into the formula, we find that the rise in temperature is approximately 225.0 degrees Celsius."
    },
    {
        "instruction": "If a diatomic gas of 7 moles at 54 m3 is isothermally changed to volume 29 m3 at 14 K, then what is the work done.\n",
        "input": "Work Done = n*R*T*ln(V2/V1)",
        "output": "506.3 joules\nTo calculate the work done during an isothermal expansion of a diatomic gas, we can use the following equation: Work done = n * R * T * ln(V2/V1), where n is the number of moles of the gas, R is the ideal gas constant (approximately 8.314 J/(mol\u00b7K)), T is the temperature in Kelvin, V1 is the initial volume, and V2 is the final volume."
    },
    {
        "instruction": "A coil of inductance 0.59 H and resistance 65 ohm is connected to a 234 V, 32 Hz ac supply. What is the time lag between voltage maximum and current maximum?",
        "input": "Time_lag = atan((f * L * 2 * pi) / R) / (2 * pi * f)",
        "output": "5.32e-03 s"
    },
    {
        "instruction": "A 87 pF capacitor is charged by a 80 V supply. It is then disconnected from the supply and is connected to another uncharged 37 pF capacitor. How much electrostatic energy is lost in this process?",
        "input": "Formula: (278400.0 - 83070.96774193548) * 10^(-12)\nValues: c1 = 87 pF, c2 = 37 pF, v = 80 V",
        "output": "Answer:1.95e-07 joule\n\nExplanation: The electrostatic energy lost in the process can be calculated by subtracting the final energy from the initial energy:\n\nE_loss = E_initial - E_final\n\nThe initial energy E_initial can be calculated as 0.5 * C1 * V^2, where C1 is the capacitance of the first capacitor and V is the voltage. The final energy E_final can be calculated as 0.5 * C3 * V^2, where C3 is the equivalent capacitance when the two capacitors are combined.\n\nSubstituting the given values, we have:\n\nE_loss = 278400.0 joule - 83070.96774193548 joule = E_loss = 1.95e-07 joule joule."
    },
    {
        "instruction": "A power transformer line feeds input power at 29312 V to a stepdown transformer with its primary windings having 1408 turns. What should be the number of turns in the secondary in order to get output at 229 V?",
        "input": "N_secondary = (N_primary * V_primary) / V_secondary",
        "output": "11 turns"
    },
    {
        "instruction": "A meter stick is balanced on a knife edge at its center. When two coins, each of mass 90 g and 77 g respectively, are put at the 23 mark and 87 mark respectively, the stick is found to be balanced at 46 cm. What is the mass of the meter stick?",
        "input": "Mass = (Right Side - Left Side) / Distance",
        "output": "The mass of the meter stick is approximately -271.8 g.\nLeft Side = m1 * (t3 - t1) = 90 * (46 - 23)\nRight Side = m2 * (t2 - t3) = 77 * (87 - 46)"
    },
    {
        "instruction": "What is the magnitude and direction of (914) i + (1119) j?",
        "input": "magnitude = sqrt(914^2 + 1119^2), direction = atan(1119/914) * (180 / pi)",
        "output": "The magnitude is 1444.8 and the direction is 51 degrees with the positive x-axis."
    },
    {
        "instruction": "Two lamps, one rated 76 W at 231 V, and the other 63 W at 234 V, which has more resistance?",
        "input": "",
        "output": "lamp2"
    },
    {
        "instruction": "An object is placed at 812 cm in front of a convex lens. Image is formed at a distance of 1651 cm in front of it. Find the focal length of the lens.",
        "input": "Formula: 1/f = 1/v - 1/u for convex lens.",
        "output": "To find the focal length of the lens, we use the formula for convex lenses: 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for f. In this case, the focal length of the lens is 1597.9 cm., this is the final The focal length of the lens is 1597.9 cm."
    },
    {
        "instruction": "A convex lens produces a virtual image of height 3 cm at a distance of 92 cm from it of a real object having a height of 56 cm. At what distance is the object placed from the lens?",
        "input": "Formula: u = (v * ho) / hi",
        "output": "To find the distance at which the object is placed from the lens, we use the formula u = (v * ho) / hi, where u is the distance of the object from the lens, v is the distance of the image from the lens, hi is the height of the image, and ho is the height of the object. By substituting the given values into the formula, we can calculate u. In this case, the object is placed at a distance of 1717.3 cm from the lens., this is the final The object is placed at a distance of 1717.3 cm from the lens."
    },
    {
        "instruction": "A refrigerator is to maintain eatables kept inside at 133 K, if room temperature is 325 K. Calculate the coefficient of performance.\n",
        "input": "Coefficient of performance = T2/T1-T2",
        "output": "0.7\nThis formula is only applicable if the refrigerator is based on the Carnot Cycle."
    },
    {
        "instruction": "An oxygen cylinder of volume 40 litre has an initial gauge pressure of 21 atmosphere and a temperature of 31 degree C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 17 atmosphere and its temperature drops to 50 degree C. Estimate the number of moles of oxygen taken out of the cylinder. (R = 8.3 J mol-1 K-1)",
        "input": "n = (p1 * V) / (R * T1) - (p2 * V) / (R * T2)",
        "output": "7.9 mol \n \np1 = initial pressure\np2 = final pressure\nV = volume\nt1 = initial temperature\nt2 = final temperature\nR = gas constant\nn = (21 * 40 * 10^5) / (8.31 * 304) - (17 * 40 * 10^5) / (8.31 * 323)\nn = 33251.0 - 25334.1\nn = 7916.9\nn = 7.9 mol"
    },
    {
        "instruction": "A rod of mass 8867 kg has a length of 6 m. What is the moment of inertia with respect to its end?",
        "input": "Moment of Inertia = (Constant) * mass * length^2",
        "output": "The moment of inertia with respect to its end is approximately 106404.0 kgm^2.\n\nMoment of Inertia = (Constant) * mass * length^2\n\nConstant = 0.3333333333333333\nmass = 8867 kg\nlength = 6 m"
    },
    {
        "instruction": "Two point charges q1 = 196 x 10^(-6)C and q2 = 195 x 10^(-6)C are located 58 cm apart in vacuum. What is the electric field at the midpoint O of the line joining two charges?\n",
        "input": "Electric field = (q1 - q2) / (4 * pi * epsilon * r^2)",
        "output": "To calculate the electric field at the midpoint O, we use the formula:\nElectric field = (q1 - q2) / (4 * pi * epsilon * r^2)\nGiven q1 = 196 x 10^(-6)C, q2 = 195 x 10^(-6)C, and r = 58 cm,\nElectric field = 1.07e+05 newton/coulomb\n"
    },
    {
        "instruction": "On a long horizontally moving belt, a child runs to and fro with a speed of 77 ms-1 (with respect to the belt) between his parents located 148 m apart on the moving belt. The belt moves with a speed of 37 ms-1. For an observer on a stationary platform outside, what is the speed of the child running opposite to the direction of motion of the belt?",
        "input": "speed_child = speed_relative - speed_belt",
        "output": "The speed of the child running opposite to the direction of motion of the belt is 40 ms-1."
    },
    {
        "instruction": "A body describes simple harmonic motion with an amplitude of 338 mm and a period of 51 ms. Find the acceleration of the body when the displacement is 144 mm?\n",
        "input": "w*w*amp",
        "output": "Using this formula: w*w*amp, this is the final answer derived: 2.19e+06 ms-2\n"
    },
    {
        "instruction": "In a double-slit experiment the angular width of a fringe is found to be 0.1 degrees on a screen placed 6 m away. The wavelength of light used is 67 nm. What will be the angular width of the fringe if the entire experimental apparatus is immersed in liquid of refractive index 1.97.\n",
        "input": "refractive index = angular width before immersing in water/angular width after immersing in water",
        "output": "5.08e-02 degrees\nTo calculate the angular width of a fringe when the entire experimental apparatus is immersed in a liquid of refractive index (\u03bc), we need to consider the effect of the refractive index on the wavelength of light.we can calculate the angular width of the fringe in the liquid (\u03b82') using the formula: \u03b82' = sin^(-1)(\u03bb' / d), where d is the distance to the screen (D) in meters."
    },
    {
        "instruction": "What is the energy associated with a mass of 163.8 g ?\n",
        "input": "Energy = Mass*c^2",
        "output": "1.47e+16joule\nTo calculate the energy associated with a mass, we need to specify the type of energy we are referring to. There are various forms of energy, such as kinetic energy, potential energy, thermal energy, etc. If we assume you are referring to the energy associated with the mass in terms of its rest energy, we can use Einstein's mass-energy equivalence principle, given by the equation: E = m * c^2"
    },
    {
        "instruction": "A charge of 14 mC is located at the origin. Calculate the work done in taking a charge 19 nC from a point P(0, 0, 17 cm) to a point Q(0, 13 cm, 0), via a point R(0, 14 cm, 6 cm).",
        "input": "Charge at Origin (q1) = 14 mC + Charge at P (q2) 19 nC + Coordinates of P: (0, 0, 17 cm) + Coordinates of Q : (0, 13 cm, 0) + Coordinates of R : (0, 14 cm, 6 cm)",
        "output": "4.33e-02 joule\nExplanation: The work done in moving a charge between two points is given by the formula W = q1 * q2 * (Vp - Vq), where q1 and q2 are the charges, and Vp and Vq are the potentials at the respective points. The potential difference (Vp - Vq) is calculated as 0.009 * (1 / p - 1 / q). Plugging in the values, we get W = 4.33e-02 joule."
    },
    {
        "instruction": "Two moving coil meters M1 and M2 have the following particulars R1 = 5 ohms, N1 = 3, A1 = 0.001 m2 , B1 = 1 T, K1 = 1 and  R2 = 1 ohms, N2 = 2 , A1 = 0.0008 m2 , B1 = 6 T, K2 = 3. Determine the ratio of current sensitivities of M1 and M2.\n",
        "input": "Ratio of current sensitivity of M1 to M2 is given by, n1 x b1 x a1 x k2 : n2 x b2 x a2 x k1",
        "output": "Ratio of current sensitivity of M1 to M2 is given by, n1 x b1 x a1 x k2 : n2 x b2 x a2 x k1 = 3 x 1 x 0.001 x 3 : 2 x 6 x 0.0008 x 1 = 0.9\n"
    },
    {
        "instruction": "Light enters from air to glass having refractive index 2221.07. If the speed of light in vacuum is 3 x 10^8 m/s, what is the speed of light in the glass?",
        "input": "Refractive Index (n) = c / v",
        "output": "The refractive index of a material is defined as the ratio of the speed of light in vacuum to the speed of light in the material. It can be calculated using the formula n = c / v, where n is the refractive index, c is the speed of light in vacuum, and v is the speed of light in the material., this is the final 135070.0 m/s"
    },
    {
        "instruction": "What is the gravitational force between two masses 81000 kg and 23000 kg seperated bt a distance 27 m.\n",
        "input": "f = (g x m1 x m2)/d^2",
        "output": "the gravitational between two bodies of masses m1 and m2 seperated by a distance d is given by, f = (g x m1 x m2)/d^2 = (6.67 x 10^-11 x 81000 x 10^-3 x 23000 x 10^-3)/27^2 = 1.70e-04 newton\n"
    },
    {
        "instruction": "The escape speed of a projectile on the Earth's surface is 11.2 km/s. A body is projected out with the speed of 174.173 km/s. What is the speed of the body far away from the Earth?",
        "input": "Projectile Speed : 173.8 km/s km/s",
        "output": "173.8 km/s\n\nExplanation: The speed of the body far away from the Earth, when projected with a speed of 173.8 km/s km/s, can be calculated using the escape speed formula. By substituting the given values, the speed is found to be 173.8 km/s."
    },
    {
        "instruction": "A meter stick of mass 18 g is balanced on a knife edge at its center. Where will the stick be balanced when a coin of mass 7 g is put at the 3 mark?",
        "input": "Balance Position = ((50 * m) + (m1 * t1)) / (m + m1)",
        "output": "The stick will be balanced at approximately 36.8 cm.\nBalance Position = ((50 * 18) + (7 * 3)) / (18 + 7)"
    },
    {
        "instruction": "A capacitor made of two circular plates of radius 69 cm, and separated by 125 cm. The capacitor is being charged by an external source. The charging current is constant and equal to 196 mA. Calculate the capacitance between the plates?",
        "input": "r = 69 cm, s = 125 cm",
        "output": "1.06e-11 farad\n\nThe capacitance of a capacitor can be calculated using the formula: C = (\u03b5\u03c0r\u00b2) / s, where \u03b5 is the permittivity of free space, r is the radius of the plates, and s is the separation between the plates."
    },
    {
        "instruction": "The electrostatic force on a small sphere of charge -0.000186 C due to another small charge of -0.000122 C in air is 195 N. What is the distance between the spheres?\n",
        "input": "r = sqrt(abs((q1 * q2 * k) / F))",
        "output": "The distance between the spheres is 1.02e+00 m\n"
    },
    {
        "instruction": "Suppose there existed a planet that went around the Sun 2555/2769 times as fast as the Earth. What would be its orbital size as compared to that of the Earth?",
        "input": "Orbital Size Ratio = (T_p / T_e)^(2/3) = (2555/2769)^(2/3)",
        "output": "The orbital size of the planet compared to that of the Earth would be approximately 0.9 times faster than Earth."
    },
    {
        "instruction": "A SONAR system fixed in a submarine operates at a frequency 38650 Hz. An enemy submarine moves towards the SONAR with a speed of 204 kmph. What is the frequency of sound reflected by the submarine? Take the speed of sound in water to be 1450 ms-1.\n",
        "input": "Apparent frequency = [(Speed of sound in air + Speed of enemy submarine)/Speed of sound in air]*Original Frequency",
        "output": "4.18e+04 hertz\nTo calculate the frequency of sound reflected by the submarine in the SONAR system, we need to consider the Doppler effect due to the relative motion between the submarines. The Doppler effect accounts for the change in frequency observed when the source of sound and the observer are in relative motion.The formula to calculate the frequency observed by the submarine is: f' = f * (v_sound / (v_sound - v_sub)), where f' is the observed frequency, f is the emitted frequency, v_sound is the speed of sound in water, and v_sub is the velocity of the submarine."
    },
    {
        "instruction": "What is the lowest total resistance that can be secured by combinations of three coils of resistance 25, 139, 28?",
        "input": "R_total = (R1 * R2 * R3) / (R1 * R2 + R2 * R3 + R3 * R1)",
        "output": "The lowest combination of resistances can be obtained by connecting them in parallel. The total resistance is calculated as (25 * 139 * 28) / (25 * 139 + 139 * 28 + 28 * 25) = 12.1 ohm.\n\nTo calculate the lowest combination of resistances, we connect them in parallel. The total resistance (R_total) is given by the formula (R1 * R2 * R3) / (R1 * R2 + R2 * R3 + R3 * R1), where R1, R2, and R3 are the individual resistances."
    },
    {
        "instruction": "A wheel starting with an initial angular velocity of 71 rad/s accelerates with a constant angular acceleration of 50 rad/s\u00b2. If it reaches an angular position of 32 rad, then what is its final velocity?",
        "input": "final_angular_velocity = sqrt(initial_angular_velocity^2 + (2 * angular_acceleration * angular_position))",
        "output": "To calculate the final angular velocity, we use the following formula:\n\nfinal_angular_velocity = sqrt(initial_angular_velocity^2 + (2 * angular_acceleration * angular_position))\n\nSubstituting the given values into the formula, we find that the final angular velocity is approximately 90.8 rad/s."
    },
    {
        "instruction": "Four point charges q1 = -13 x 10^(-6) C, q2 = -3 x 10^(-6) C, q3 = 12 x 10^(-6) C, q4 = 14 x 10^(-6) C, are located at corners of square ABCD of side 12 cm. What is the force on a charge of -2 x 10^(-6) C placed at the centre of the square?\n",
        "input": "Force (F) = k * |q1 - q3| * |q2 - q4| * q_c / (d^2)",
        "output": "To calculate the force on the charge placed at the center of the square, we use the formula for electric force between two point charges:\nForce (F) = k * |q1 - q3| * |q2 - q4| * q_c / (d^2)\nwhere k is Coulomb's constant (9 * 10^9 N\u00b7m\u00b2/C\u00b2), q1, q2, q3, q4 are the charges at the corners of the square (in Coulombs), q_c is the charge placed at the center of the square (in Coulombs), and d is the side length of the square (in meters).\nGiven q1 = -13 x 10^(-6) C, q2 = -3 x 10^(-6) C, q3 = 12 x 10^(-6) C, q4 = 14 x 10^(-6) C, d = 12 cm, and q_c = -2 x 10^(-6) C:\nForce (F) = -3.78e+01 N\n"
    },
    {
        "instruction": "On an unknown scale, the temperature of the melting point and boiling point of water is 84 degrees and 367 degrees respectively. If the temperature on the Celsius scale is 35 degrees Celsius, what is the temperature shown on that scale?",
        "input": "Temperature on the unknown scale = (((t2 - t1) * (t - ta)) / (tb - ta)) + t1",
        "output": "To find the temperature on the unknown scale, we use the following formula:\n\nTemperature on the unknown scale = (((t2 - t1) * (t - ta)) / (tb - ta)) + t1\n\nSubstituting the given values into the formula, we find that the temperature on the unknown scale is approximately 183.1."
    },
    {
        "instruction": "A concave lens produces 71 times diminished real image of height 88.58 cm of an object placed in front of it. What is the height of the object?",
        "input": "Formula: ho = n * hi",
        "output": "To find the height of the object, we use the formula ho = n * hi, where ho is the height of the object, hi is the height of the image, and n is the magnification factor. By substituting the given values into the formula, we can solve for ho. In this case, the height of the object is 6289.2 cm., this is the final The height of the object is 6289.2 cm."
    },
    {
        "instruction": "A uniformly charged conducting sphere of 90 cm diameter has a surface charge density of 78 micro-C/m\u00b2, then find the electric flux leaving the sphere?\n",
        "input": "Electric flux = Surface charge density * Surface area * (1 / (4 * pi * epsilon_0))",
        "output": "To calculate the electric flux leaving the sphere, we use the formula:\nElectric flux = Surface charge density * Surface area * (1 / (4 * pi * epsilon_0))\nGiven surface charge density = 78 micro-C/m\u00b2, diameter = 90 cm,\nElectric flux = 2.24e+07 N\u00b7m\u00b2/C\n"
    },
    {
        "instruction": "What is the time period of the SHM with equation (42)*sin(-1wt) + (-11)*cos(-1wt)?\n",
        "input": "Equation: (42)*sin(-1wt) + (-11)*cos(-1wt)",
        "output": "Using this formula: Equation: (42)*sin(-1wt) + (-11)*cos(-1wt), this is the final answer derived: 2\u03c0/1w sec\n"
    },
    {
        "instruction": "A rod of mass 300 kg rotates about its end with angular speed 23 rad/s. The length of the rod is 33 m. What is the magnitude of angular momentum of the rod about its end?",
        "input": "Angular Momentum = c * m * r\u00b2 * w",
        "output": "To calculate the magnitude of the angular momentum, we use the following formula:\n\nAngular Momentum = c * m * r\u00b2 * w\n\nWhere,\n- c = Constant for the object\n- m = Mass of the object\n- r = Radius or length of the object\n- w = Angular speed of the object\n\nThe value of the constant (c) depends on the type of object being considered:\n- For a solid cylinder: c = 1/2\n- For a solid sphere: c = 2/5\n- For a hollow sphere: c = 2/3\n- For a rod: c = 1/3\n\nSubstituting the given values into the formula, we find that the magnitude of the angular momentum is approximately 2504700.0 kg\u00b7m\u00b2."
    },
    {
        "instruction": "If a 777 V battery is connected across a resistance of 136 ohm, then find the current in the circuit?",
        "input": "Current = Voltage / Resistance",
        "output": "5.7 ampere\n\nThe current in the circuit can be calculated using Ohm's law formula, where Current = Voltage / Resistance."
    },
    {
        "instruction": "An object is placed at 708 cm in front of a convex lens of focal length 19 cm. Find at what distance image is formed and its nature.",
        "input": "Formula: 1/f = 1/v - 1/u for convex lens.",
        "output": "To find the distance of the image formed, we use the formula for convex lenses: 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for v. In this case, the image is real and located at a distance of 19.5 cm., this is the final The image is formed at 19.5 cm and it is real."
    },
    {
        "instruction": "Torque of 539 Nm is transmitted to an engine at a power of 324 W. What is the angular speed of the rotor?",
        "input": "Angular Speed = Power / Torque",
        "output": "Angular Speed = 324 W / 539 Nm\n\nTo calculate the angular speed of the rotor, we use the following formula:\n\nAngular Speed = Power / Torque\n\nSubstituting the values:\n\nPower = 324 W\nTorque = 539 Nm\n\nWe find that the angular speed of the rotor is 0.6 rad/s."
    },
    {
        "instruction": "Two objects of masses 4 g and 3 g are moving along the same line and direction with velocities of 6 m/s and 1 m/s respectively. They collide and after the collision, the second object moves at a velocity of 17 m/s. Determine the initial velocity of the second object.",
        "input": "u2 = ((m1 * v1) + (m2 * v2) - (m1 * u1)) / m2",
        "output": "To find the initial velocity of the second object (u2), we use the formula:\n\nu2 = ((m1 * v1) + (m2 * v2) - (m1 * u1)) / m2\n\nSubstituting the given values, we have:\n\nu2 = ((4 * 17) + (3 * 3) - (4 * 6)) / 3\n\nSimplifying the expression gives us u2 = 17.7 m/s."
    },
    {
        "instruction": "A heating element using nichrome connected to a 222 V supply draws an initial current of 1089 mA which settles after a few seconds to a steady value of 900 mA. What is the steady temperature of the heating element if room temperature is 27 degree C (temp coeff of nichrome is 1.70 x 10^(-4) degree C-1)?",
        "input": "T = ((R2 - R1) / (R1 * temp_coeff)) + T_room",
        "output": "1262 degree centigrade\n\nTo calculate the steady temperature of the heating element, use the formula: T = ((R2 - R1) / (R1 * temp_coeff)) + T_room, where R2 is the resistance with steady current, R1 is the resistance with initial current, temp_coeff is the temperature coefficient, and T_room is the room temperature."
    },
    {
        "instruction": "A vertical off-shore structure is built to withstand a maximum stress of 9800000 Pa. Is the structure suitable for putting up on top of an oil well in the ocean? Take the depth of the ocean to be roughly 10 km, and ignore ocean currents?",
        "input": "10 * 1000 * 980",
        "output": "no, it is not suitable"
    },
    {
        "instruction": "A series LCR circuit is connected to a variable frequency 230 V source with L = 190 H, C = 94 muF, R = 114 ohm. Determine the RMS potential drop across inductance?",
        "input": "RMS Potential Drop across Inductance = Current RMS * \u03c9_r * L",
        "output": "RMS Potential Drop across Inductance = 2.87e+03 V"
    },
    {
        "instruction": "An Electric Iron takes a current of 4 A, if 1337 J of heat is developed in 21 s, then what is the value of its resistance?",
        "input": "R = energy / (I^2 * t)",
        "output": "To calculate the resistance, we rearrange the formula R = energy / (I^2 * t) to solve for R. Substituting the values, where energy is 1337 J, I is 4 A, and t is 21 s, we can calculate the resistance., this is the final answer 4.0"
    },
    {
        "instruction": "Assuming the Earth to be a sphere of uniform mass density, how much would a body weigh 44/87 down to the center of the Earth if it weighed 700 N on the surface?",
        "input": "Weight on the Surface (W) = 700 N, Height Ratio (n/d) = 44/87",
        "output": "The weight of the body 44/87 down to the center of the Earth, assuming a uniform mass density, would be 346.0 newtons."
    },
    {
        "instruction": "A force is applied on a body of mass 53 kg placed on a smooth surface resulting in acceleration of 804 m/s^2, then what is the force applied?",
        "input": "F = m * a",
        "output": "42612\nTo calculate the force, we use the formula F = m * a, where F is the force, m is the mass (53 kg), and a is the acceleration (804 m/s^2)."
    },
    {
        "instruction": "Estimate the fraction of molecular volume to the actual volume occupied by a gas at STP. Take the diameter of the gas molecule to be 569.7 A.",
        "input": "(4 * pi * d * d * d * 1000 * n) / (3 * 8 * 22.4)",
        "output": "2.6031675717231454e+33 \n (4 * pi * d * d * d * 1000 * n) / (3 * 8 * 22.4)"
    },
    {
        "instruction": "A string of mass 49 kg is under a tension of 563 N. The length of the stretched string is 54 m. If the transverse jerk is struck at one end of the string, how long does the disturbance take to reach the other end?\n",
        "input": "Speed^2 = Tension*length/mass",
        "output": "2.17e+00 s\nTo determine the time it takes for a disturbance to travel from one end of a string to the other, we can use the wave speed equation for transverse waves on a string. The wave speed (v) on a string is given by: v = sqrt(T / \u03bc), where T is the tension in the string and \u03bc is the linear mass density of the string, which is given by the mass per unit length (\u03bc = m / l)."
    },
    {
        "instruction": "The radius of a sphere is measured as 1701.6 +/- 9.2 cm calculate its surface area (in m2) with error limits.\n",
        "input": "Surface Area = 4\u03c0r\u00b2",
        "output": "3636.7+/-39.3\nTo calculate the surface area of a sphere with a measured radius, we use the formula: Surface Area = 4\u03c0r\u00b2. In this case, the radius of the sphere is 1701.6 cm, and the error in the measurement is 39.3 cm. To determine the error in the surface area calculation, we can use error propagation. The formula for calculating the maximum error in a function involving measured quantities is: Max Error = |dA/dx| * \u0394x, where Max Error is the maximum error, dA/dx is the derivative of the function with respect to the measured quantity (radius in this case), and \u0394x is the error in the measured quantity. Taking the derivative of the surface area formula with respect to the radius, we have: dA/dr = 8\u03c0r. Substituting the given values into the error propagation formula, we can calculate the maximum error in the surface area: Max Error = |8\u03c0r| * \u0394r. Now, we can substitute the given radius and error values to calculate the maximum error in the surface area."
    },
    {
        "instruction": "If a point on the circumference of a wheel rotating with an angular acceleration of 677 rad/s\u00b2 has an acceleration of 538 m/s\u00b2, what is the radius of the wheel?",
        "input": "radius = acceleration / angular_acceleration",
        "output": "To calculate the radius, we use the following formula:\n\nradius = acceleration / angular_acceleration\n\nSubstituting the given values into the formula, we find that the radius is approximately 0.8 m."
    },
    {
        "instruction": "If a car has an initial velocity of 470 m/s and has a constant acceleration of 10 m/s\u00b2, then what is the time taken by the car to attain a velocity of 897 m/s?",
        "input": "time = (final_velocity - initial_velocity) / acceleration",
        "output": "The time taken by the car to attain a velocity of 897 m/s is 42.7 s."
    },
    {
        "instruction": "A convex lens produces 21 times magnified virtual image of an object at a distance of 147 cm from the lens. At what distance is the object placed in front of the lens?",
        "input": "Formula: u = v / n",
        "output": "To find the distance at which the object is placed in front of the lens, we use the formula u = v / n, where u is the distance of the object from the lens, v is the distance of the image from the lens, and n is the magnification factor. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 7.0 cm in front of the lens., this is the final The object is placed at a distance of 7.0 cm in front of the lens."
    },
    {
        "instruction": "A stone is thrown vertically upward with a velocity of 518734 m/s. What is the time taken by it to reach the maximum height?",
        "input": "time = initial_velocity / acceleration",
        "output": "The time taken by the stone to reach the maximum height is 52932.0 s."
    },
    {
        "instruction": "A series LCR circuit is connected to a variable frequency 230 V source with L = 104 H, C = 93 muF, R = 175 ohm. Determine the amplitude of current at the resonating frequency?",
        "input": "Current Amplitude = V_amplitude / Impedance",
        "output": "Current Amplitude = 1.9 A"
    },
    {
        "instruction": "A hollow sphere of mass 260 kg has a radius of 15 m. What is the moment of inertia with respect to its symmetric axis?",
        "input": "Moment of Inertia = (Constant) * mass * radius^2",
        "output": "The moment of inertia with respect to its symmetric axis is approximately 39000.0 kgm^2.\n\nMoment of Inertia = (Constant) * mass * radius^2\n\nConstant = 0.6666666666666666\nmass = 260 kg\nradius = 15 m"
    },
    {
        "instruction": "The transverse displacement of a string is given by y(x, t) = 0.01 sin 9\u03c0 /5 x cos (65\u03c0 t) where x, y are in m and t in s. The length of the string is 9 m and its mass is 0.0 kg,interpret this wave as a superimposition of two waves travelling in opposite direction, give  magnitude of speed of propagation of each wave?\n",
        "input": "speed = frequency*wavelength",
        "output": "29.2 ms-1\n"
    },
    {
        "instruction": "Two gold pieces of masses are 2800 g and 99000 g respectively. What is the sum of the masses of the pieces to correct significant figures?\n",
        "input": "",
        "output": "1.1e+05\n"
    },
    {
        "instruction": "A stone tied to the end of a string 126 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 111 revolutions in 183 s, what is the magnitude and direction of acceleration of the stone?",
        "input": "a = v\u00b2/r, v = 2\u03c0r/T",
        "output": "a = 18.3 ms-2, towards the centre of the circle, v = 3.8 rad/s\n {explanation}}"
    },
    {
        "instruction": "A hollow cylinder and a solid cylinder roll down two different inclined planes of heights 13 and 9 and with angles of inclination of 73 and 40, which will reach the ground faster?",
        "input": "time = sqrt(height * (k + 1)) / sin(angle)",
        "output": "To compare the times, we use the following formula:\n\ntime = sqrt(height * (k + 1)) / sin(angle)\n\nSubstituting the given values into the formula, we find that:\n\nThe hollow cylinder takes less time to reach the ground."
    },
    {
        "instruction": "A body describes simple harmonic motion with an amplitude of 195 mm and a period of 153 ms. Find the acceleration of the body when the displacement is 191 mm?\n",
        "input": "w*w*amp",
        "output": "Using this formula: w*w*amp, this is the final answer derived: 3.22e+05 ms-2\n"
    },
    {
        "instruction": "An object is projected with an initial velocity of 710 m/s. If the maximum height reached by it is 2679 m, what is the angle of projection?",
        "input": "",
        "output": "19 degrees w.r.t. to the ground"
    },
    {
        "instruction": "A child stands at the centre of a turntable with his arms outstretched. The turntable is rotating with an angular speed of 56 rad/s. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to 6/82 times the initial value?",
        "input": "Angular Speed = (n2 * w) / n1\nKinetic Energy Ratio = (n2^3) / (n1^3)",
        "output": "To calculate the angular speed and kinetic energy ratio, we use the following formulas:\n\nAngular Speed = (n2 * w) / n1\nKinetic Energy Ratio = (n2^3) / (n1^3)\n\nWhere,\n- n1 = Initial moment of inertia\n- n2 = Reduced moment of inertia\n- w = Initial angular speed\n\nSubstituting the given values into the formulas, we find that the angular speed of the child is approximately 765.3 rad/s rad/s."
    },
    {
        "instruction": "12 capacitors each of capacitance 340pF are connected in series. What is the total capacitance of the combination when the system is connected to a 8 V supply?\n",
        "input": "1 / C_total = 1 / C1 + 1 / C2 + 1 / C3 + ... + 1 / Cn\n",
        "output": "2.83e+01 pico-farad\n\nExplanation: 1 / C_total = 1 / 340 + 1 / 340 + 1 / 340 + ... + 1 / 340\n"
    },
    {
        "instruction": "The coefficient of volume expansion of brass is 6.000000000000001e-05 K^-1. What is the change in its volume 88 m^3 for a rise in temperature from 61 degree C to 307 degree C?",
        "input": "Change in volume = d1 * a * (t2 - t1)",
        "output": "To find the change in volume, we use the following formula:\n\nChange in volume = d1 * a * (t2 - t1)\n\nSubstituting the given values into the formula, we find that the change in volume is approximately 1.3 m^3."
    },
    {
        "instruction": "A wheel starting with an initial angular velocity of 41 rad/s accelerates with a constant angular acceleration of 77 rad/s\u00b2. If it reaches an angular position of 42 rad, then what is its final velocity?",
        "input": "final_angular_velocity = sqrt(initial_angular_velocity^2 + (2 * angular_acceleration * angular_position))",
        "output": "To calculate the final angular velocity, we use the following formula:\n\nfinal_angular_velocity = sqrt(initial_angular_velocity^2 + (2 * angular_acceleration * angular_position))\n\nSubstituting the given values into the formula, we find that the final angular velocity is approximately 90.3 rad/s."
    },
    {
        "instruction": "A convex mirror produces 74 times diminished real image of an object placed at 93 cm in front of it. At what distance is the image formed from the mirror?",
        "input": "Formula: v = u / n",
        "output": "To find the distance at which the image is formed from the mirror, we use the formula v = u / n, where v is the distance of the image from the mirror, u is the distance of the object from the mirror, and n is the magnification factor. By substituting the given values into the formula, we can calculate v. In this case, the image is formed at a distance of 1.3 cm from the mirror., this is the final The image is formed at a distance of 1.3 cm from the mirror."
    },
    {
        "instruction": "A bar magnet of magnetic moment 0.13 J/T is kept in a uniform magnetic field of 0.08 T. What is the work done by an external torque to turn the magnet which is aligned at an angle of 64 degrees with the magnetic field to an angle of 149 degrees?",
        "input": "-m * b * (d1 - d2)",
        "output": "The work done by an external torque to turn the magnet aligned at an angle of 0.43837114678907746 degrees with the magnetic field to an angle of -0.8571673007021122 degrees can be calculated using the formula -m * b * (d1 - d2), where 'm' is the magnetic moment of the magnet, 'b' is the magnetic field strength, 'd1' is the initial angle, and 'd2' is the final angle. Substituting the given values, we have -(0.13) * 0.08 * (0.44 - -0.86)."
    },
    {
        "instruction": "Assume an unknown planet of orbital period 343 days is rotating around the sun with an orbit of radius 1217 * 10^8 m. What is the ratio of the mass of the sun to the mass of the unknown planet?",
        "input": "Mass Ratio = ((R_earth^3) * (T_planet^2)) / ((R_planet^3) * (T_earth^2)) = ((149.6 * 10^8)^3 * (343^2)) / ((1217 * 10^8)^3 * (365.25^2))",
        "output": "The ratio of the mass of the sun to the mass of the unknown planet is approximately 0.0."
    },
    {
        "instruction": "A solid sphere of mass 9193 kg has a radius of 9 m. What is the moment of inertia with respect to its symmetric axis?",
        "input": "Moment of Inertia = (Constant) * mass * radius^2",
        "output": "The moment of inertia with respect to its symmetric axis is approximately 297853.2 kgm^2.\n\nMoment of Inertia = (Constant) * mass * radius^2\n\nConstant = 0.4\nmass = 9193 kg\nradius = 9 m"
    },
    {
        "instruction": "A bat is flitting about in a cave, navigating via ultrasonic beeps. Assume that the sound emission frequency of the bat is 24520 Hz. During one fast swoop directly toward a flat wall surface, the bat is moving at 0.0727 times the speed of sound in air. What is the apparent frequency of the sound striking the wall?\n",
        "input": "apparent frequency = [{(speed of air + speed of bat)}/speed of air]*apparent frequency of sound striking the wall",
        "output": "2.64e+04 hertz\nThe concept of Doppler's effect has been applied to calculate apparent frequencies."
    },
    {
        "instruction": "A hollow cylinder of mass 6574 kg has a radius of 94 m. What is the moment of inertia with respect to its symmetric axis?",
        "input": "Moment of Inertia = (Constant) * mass * radius^2",
        "output": "The moment of inertia with respect to its symmetric axis is approximately 58087864 kgm^2.\n\nMoment of Inertia = (Constant) * mass * radius^2\n\nConstant = 1\nmass = 6574 kg\nradius = 94 m"
    },
    {
        "instruction": "An object is placed at 356 cm in front of a concave lens of focal length 509 cm. Find at what distance image is formed and its nature.",
        "input": "Formula: 1/f = 1/v - 1/u for concave lens.",
        "output": "This is the answer The image is formed at 209 cm and it is virtual., formula used is : Formula: 1/f = 1/v - 1/u for concave lens."
    },
    {
        "instruction": "An object is placed at 971 cm in front of a concave mirror. Image is formed at a distance of 1916 cm behind it. Find the focal length of the mirror.",
        "input": "Formula: 1/f = 1/u - 1/v",
        "output": "To find the focal length of the mirror, we use the formula 1/f = 1/u - 1/v, where f is the focal length, u is the distance of the object, and v is the distance of the image. By substituting the given values into the formula, we can solve for f. In this case, the focal length of the mirror is 1968.7 cm., this is the final 1968.7"
    },
    {
        "instruction": "What is the gravitational force between two masses 38000 kg and 89000 kg seperated bt a distance 85 m. G = 6.67 x 10-11\n",
        "input": "f = (g x m1 x m2)/d^2",
        "output": "the gravitational between two bodies of masses m1 and m2 seperated by a distance d is given by, f = (g x m1 x m2)/d^2 = (6.67 x 10^-11 x 38000 x 10^-3 x 89000 x 10^-3)/85^2 = 3.12e-05 newton\n"
    },
    {
        "instruction": "A wheel starting with an initial angular velocity of 75 rad/s accelerates with a constant angular acceleration of 46 rad/s\u00b2. If it reaches an angular position of 61 rad, then what is its final velocity?",
        "input": "final_angular_velocity = sqrt(initial_angular_velocity^2 + (2 * angular_acceleration * angular_position))",
        "output": "To calculate the final angular velocity, we use the following formula:\n\nfinal_angular_velocity = sqrt(initial_angular_velocity^2 + (2 * angular_acceleration * angular_position))\n\nSubstituting the given values into the formula, we find that the final angular velocity is approximately 106.0 rad/s."
    },
    {
        "instruction": "What is the phase of the SHM with equation (-91)*sin(-51wt) + (133)*cos(-51wt)? (i.e., if written as Asin(bwt+theta), then what is the value of theta)\n",
        "input": "Equation: (-91)*sin(-51wt) + (133)*cos(-51wt)",
        "output": "Using this formula: Equation: (-91)*sin(-51wt) + (133)*cos(-51wt), this is the final answer derived: -56 degrees\n"
    },
    {
        "instruction": "Find the power of a convex lens whose focal length is 2474.11 cm.",
        "input": "Formula: P = 100 / f",
        "output": "To find the power of a convex lens, we use the formula P = 100 / f, where P is the power and f is the focal length. By substituting the given value of f into the formula, we can solve for P. In this case, the power is 0.0 diatrope., this is the final 0.0"
    },
    {
        "instruction": "Suppose that the electric field amplitude of an electromagnetic wave is E0 = 1410 N/C and that its frequency is v = 1141 MHz. Find an expression for B?",
        "input": "B0 = 4.70e-06 tesla, k = 2.39e+01 rad/m, w = 7.17e+09 rad/s",
        "output": "4.70e-06sin[2.39e+01x-7.17e+09t]\n\nThe expression for the magnetic field (B) of an electromagnetic wave can be written as B = B0sin(kx - wt)."
    },
    {
        "instruction": "A particle has a velocity of 6308 m/s and wavelength 3.3730000000000004e-07 A. Find its mass.\n",
        "input": "Mass = h/wavelength*velocity",
        "output": "0.0kg\nTo find the mass of the particle, we can use the de Broglie wavelength equation: \u03bb = h / (m * v) where \u03bb is the wavelength, h is the Planck constant (approximately 6.626 x 10^-34 J\u00b7s), m is the mass of the particle, and v is its velocity."
    },
    {
        "instruction": "Find the value of g using simple pendulum, the following observations were made: length of thread l = 244 +/- 10 cm, time period of oscillation T = 0.49 +/- 0.01 s, then value of g in error limits is?\n",
        "input": "g = (4\u03c0\u00b2l) / T\u00b2",
        "output": "40079.01+/-3278.46\nTo find the value of acceleration due to gravity (g) using a simple pendulum, we can use the formula: g = (4\u03c0\u00b2l) / T\u00b2, where l is the length of the pendulum and T is the time period of oscillation. In this case, the length of the pendulum is 244 cm, and the time period of oscillation is 0.49 s. The error in the length measurement is 10 cm, and the error in the time period measurement is 0.01 s. To determine the error in the calculated value of g, we can use error propagation. The formula for calculating the maximum error in a function involving measured quantities is: Max Error = |dg/dx| * \u0394x, where Max Error is the maximum error, dg/dx is the derivative of the function with respect to the measured quantity (length or time period), and \u0394x is the error in the measured quantity. Taking the derivatives of the g formula with respect to length and time period, we have: dg/dl = (4\u03c0\u00b2) / T\u00b2, dg/dT = -(8\u03c0\u00b2l) / T\u00b3. Substituting the given values into the error propagation formula, we can calculate the maximum error in the value of g: Max Error = |(4\u03c0\u00b2 / T_val\u00b2) * l_error| + |(-(8\u03c0\u00b2l_val) / T_val\u00b3) * t_error. Now, we can substitute the given values to calculate the value of g and its maximum error within the error limits of length and time period."
    },
    {
        "instruction": "Two trains A and B of length 65 m each are moving on two parallel tracks with a uniform speed of 799 m/s in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by 1 m/s\u00b2. If after 30 s, the guard of B just brushes past the driver of A, what was the original distance between them?",
        "input": "separation distance = (1 / 2) * acceleration * (time ** 2)",
        "output": "acceleration of B is 1 m/s\u00b2, time taken by B to cover the separation distance is 30 s, length of each train is 65 m, speed of each train is 799 m/sThe original distance between the two trains is 320.0 m.\n\nseparation distance = (1 / 2) * acceleration * (time ** 2)\n\nThe separation distance between the two trains is the distance covered by the guard of B in the time interval of 30 s. The guard of B covers this distance in the time interval of 30 s with an acceleration of 1 m/s\u00b2. The original distance between the two trains is the separation distance minus the sum of the lengths of the two trains."
    },
    {
        "instruction": "A convex mirror produces a real image at a distance of 320 cm from it of a real object placed 340 cm in front of it. What is the magnification of the mirror?",
        "input": "Formula: m = hi / ho = v / u",
        "output": "To find the magnification of the convex mirror, we use the formula m = hi / ho = v / u, where m is the magnification, hi is the height of the image, ho is the height of the object, v is the distance of the image from the mirror, and u is the distance of the object from the mirror. By substituting the given values into the formula, we can calculate the magnification. In this case, the magnification of the mirror is 0.9., this is the final The magnification of the mirror is 0.9."
    },
    {
        "instruction": "A capacitor with air between its parallel plates, each plate has an area of 0.1374 m\u00b2 and the distance between the plates is 20 mm. If this capacitor is connected to a 311 V supply and a 20 mm thick mica sheet is inserted between the plates and then the supply is disconnected, then what will happen?",
        "input": "A = 0.1374 m\u00b2, d = 20 mm, V = 311 V",
        "output": "capacitance becomes = 6 * 6.08e+01 = 3.65e+02 pico-farad, charge remains = capacitance * V = 6.08e-11 * 311 = 1.14e-07 coulomb\n\nWhen the supply is disconnected after inserting the mica sheet, the capacitance of the capacitor remains the same, and the charge on the capacitor also remains the same."
    },
    {
        "instruction": "A meter stick is balanced on a knife edge at its center. Where will the stick be balanced when two coins, each of mass 97 g and 25 g respectively, are put at the 11 mark and 63 mark respectively?",
        "input": "Balance Position = ((50 * m) + (m1 * t1) + (m2 * t2)) / (m + m1 + m2)",
        "output": "The stick will be balanced at approximately 33.2 cm.\nBalance Position = ((50 * 84) + (97 * 11) + (25 * 63)) / (84 + 97 + 25)"
    },
    {
        "instruction": "What is the highest total resistance that can be secured by combinations of three coils of resistance 136, 93, 43?",
        "input": "R_total = R1 + R2 + R3",
        "output": "The highest combination of resistances can be obtained by connecting them in series. The total resistance is 136 + 93 + 43 = 272 ohm.\n\nTo calculate the highest combination of resistances, we add the resistances in series. The total resistance (R_total) is equal to the sum of the individual resistances (R1, R2, and R3)."
    },
    {
        "instruction": "An oxygen cylinder of volume 51 litre has an initial gauge pressure of 16 atmosphere and a temperature of 25 degree C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 9 atmosphere and its temperature drops to 37 degree C. Estimate the number of moles of oxygen taken out of the cylinder. (R = 8.3 J mol-1 K-1)",
        "input": "n = (p1 * V) / (R * T1) - (p2 * V) / (R * T2)",
        "output": "15.1 mol \n \np1 = initial pressure\np2 = final pressure\nV = volume\nt1 = initial temperature\nt2 = final temperature\nR = gas constant\nn = (16 * 51 * 10^5) / (8.31 * 298) - (9 * 51 * 10^5) / (8.31 * 310)\nn = 32951.3 - 17817.6\nn = 15133.7\nn = 15.1 mol"
    },
    {
        "instruction": "Estimate the average thermal energy of a helium atom at 59254 degree C.",
        "input": "energy = 1.5 * k * temperature",
        "output": "0.0= 1.5 * k * temperature"
    },
    {
        "instruction": "A convex lens produces a virtual image of height 92 cm at a distance of 73 cm from it of a real object having a height of 78 cm. At what distance is the object placed from the lens?",
        "input": "Formula: u = (v * ho) / hi",
        "output": "To find the distance at which the object is placed from the lens, we use the formula u = (v * ho) / hi, where u is the distance of the object from the lens, v is the distance of the image from the lens, hi is the height of the image, and ho is the height of the object. By substituting the given values into the formula, we can calculate u. In this case, the object is placed at a distance of 61.9 cm from the lens., this is the final The object is placed at a distance of 61.9 cm from the lens."
    },
    {
        "instruction": "A tank is filled with a liquid of refractive index 161 to a height of 472.4 cm. What is the apparent depth of a needle lying at the bottom of the tank?",
        "input": "Formula: apparent depth of needle = height of tank / refractive index",
        "output": "To calculate the apparent depth of the needle, we use the formula: apparent depth of needle = height of tank / refractive index. In this case, the height of the tank is 472.4 cm and the refractive index is 161., this is the final 2.93 cm"
    },
    {
        "instruction": "Two gold pieces of masses are 55900 g and 8830 g respectively. What is the difference of the masses of the pieces to correct significant figures?\n",
        "input": "",
        "output": "4.71e+04\n"
    },
    {
        "instruction": "A stone tied to the end of a string 195 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 137 revolutions in 54 s, what is the magnitude and direction of acceleration of the stone?",
        "input": "a = v\u00b2/r, v = 2\u03c0r/T",
        "output": "a = 495.5 ms-2, towards the centre of the circle, v = 15.9 rad/s\n {explanation}}"
    },
    {
        "instruction": "Suppose we employ a system of units in which the unit of mass equals 106 kg, the unit of length equals 27 m, the unit of time is 4 s, then value of 7 pascal in new system\n",
        "input": "7 Pa = (Force N) / (Area m\u00b2) = [(m kg) * (l m) / (t\u00b2 s\u00b2)] / [(l m)\u00b2]",
        "output": "28.53\nTo find the value of 7 pascals in the given system of units, we need to consider the relationships between the units of mass (kg), length (m), time (s), and pressure (Pascal). In the new system of units, we have: 1 unit of mass = 28.53\n kg, 1 unit of length = 27 m, 1 unit of time = 4 s. To find the value of 7 pascals, we need to determine the conversion factors between the new system and the standard SI units. The pressure (Pascal) can be expressed as: 7 Pa = (Force N) / (Area m\u00b2) = [(m kg) * (l m) / (t\u00b2 s\u00b2)] / [(l m)\u00b2] = (m * 28.53\n kg) / (t\u00b2 * 4 s\u00b2). Substituting the given values into this equation, we have: 7 Pa = (m * 28.53\n kg) / (t\u00b2 * 4 s\u00b2). Simplifying this expression will give us the value of 7 pascals in the new system of units."
    },
    {
        "instruction": "A long straight wire in the horizontal plane carries a current of of 76 A in north to south direction. What is the magnitude and direction of the magnetic field B at a point 1356 cm west of the wire.\n",
        "input": "B = (mu * i) / (2 * pi * r)",
        "output": "To calculate the magnitude and direction of the magnetic field B, we use the following formula:\n\nB = (mu * i) / (2 * pi * r)\n\nWhere,\n- B = Magnetic field\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- i = Current flowing through the wire\n- r = Distance from the wire\n\nSubstituting the given values into the formula, we find that the magnitude and direction of the magnetic field B is approximately 1.1e-06 tesla vertically downwards\n."
    },
    {
        "instruction": "A convex lens produces 97 times diminished real image of an object at a distance of 20.27 cm from the lens. At what distance is the object placed in front of the lens?",
        "input": "Formula: u = v * n",
        "output": "To find the distance at which the object is placed in front of the lens, we use the formula u = v * n, where u is the distance of the object from the lens, v is the distance of the image from the lens, and n is the magnification factor. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 1966.2 cm in front of the lens., this is the final The object is placed at a distance of 1966.2 cm in front of the lens."
    },
    {
        "instruction": "A 100 kW drilling machine is used to drill a bore in a small aluminium block of mass 9 kg. How much is the rise in temperature of the block in 7 minutes, assuming 47 percent of power is used up in heating the machine itself or lost to the surroundings? Specific heat of aluminium = 0.91 J g-1 K-1.",
        "input": "Rise in temperature = (p * P * t) / (m * s)",
        "output": "To calculate the rise in temperature, we use the following formula:\n\nRise in temperature = (p * P * t) / (m * s)\n\nSubstituting the given values into the formula, we find that the rise in temperature is approximately 4017.1 degrees Celsius."
    },
    {
        "instruction": "A hoop of mass 5573 kg has a radius of 68 m. What is the moment of inertia with respect to its diameter?",
        "input": "Moment of Inertia = (Constant) * mass * radius^2",
        "output": "The moment of inertia with respect to its diameter is approximately 12884776.0 kgm^2.\n\nMoment of Inertia = (Constant) * mass * radius^2\n\nConstant = 0.5\nmass = 5573 kg\nradius = 68 m"
    },
    {
        "instruction": "If a particle of mass 1860 g is in linear SHM with w = 162, amplitude 11 cm then find average kinetic energy over a period.\n",
        "input": "0.25*m*0.001*w*w*amp*amp*0.0001",
        "output": "use the formula (0.25*m*0.001*w*w*amp*amp*0.0001), this is the final answer: 1.48e+02 joule\n"
    },
    {
        "instruction": "Four point charges q1 = -10 x 10^(-6) C, q2 = -13 x 10^(-6) C, q3 = -17 x 10^(-6) C, q4 = -14 x 10^(-6) C, are located at corners of square ABCD of side 16 cm. What is the force on a charge of 3 x 10^(-6) C placed at the centre of the square?\n",
        "input": "Force (F) = k * |q1 - q3| * |q2 - q4| * q_c / (d^2)",
        "output": "To calculate the force on the charge placed at the center of the square, we use the formula for electric force between two point charges:\nForce (F) = k * |q1 - q3| * |q2 - q4| * q_c / (d^2)\nwhere k is Coulomb's constant (9 * 10^9 N\u00b7m\u00b2/C\u00b2), q1, q2, q3, q4 are the charges at the corners of the square (in Coulombs), q_c is the charge placed at the center of the square (in Coulombs), and d is the side length of the square (in meters).\nGiven q1 = -10 x 10^(-6) C, q2 = -13 x 10^(-6) C, q3 = -17 x 10^(-6) C, q4 = -14 x 10^(-6) C, d = 16 cm, and q_c = 3 x 10^(-6) C:\nForce (F) = 7.46e+00 N\n"
    },
    {
        "instruction": "Two circular coils X and Y of radii 18 cm and 36 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil A has 12 turns and carries a current of 19 A, Coil B has 1 turns and carries a current of 34 A. The sense of current in X is anti-clockwise direction and in Y is clockwise direction. From an observer looking at the coils facing east, give the magnitude and direction of the net magnetic field due to the coils at the center.",
        "input": "Net magnetic field = |b1 - b2|",
        "output": "To calculate the net magnetic field, we use the following formula:\n\nNet magnetic field = |b1 - b2|\n\nWhere,\n- b1 = Magnetic field due to coil X\n- b2 = Magnetic field due to coil Y\n\nWe calculate the magnetic field for each coil using the formula:\n- Magnetic field due to coil X = (mu * n1 * i1) / (2 * r1)\n- Magnetic field due to coil Y = (mu * n2 * i2) / (2 * r2)\n\nSubstituting the given values and evaluating the formula, we find that the magnitude of the net magnetic field is approximately 7.37e-04 tesla and towards east."
    },
    {
        "instruction": "Let us assume that our galaxy consists of 201 * 10^9 stars each of one solar mass. How long will a star at a distance of 50889 ly from the galactic centre take to complete one revolution? Take the diameter of the Milky Way to be 10^5 ly.",
        "input": "No. of Stars = 201 * 10^9, Distance = 50889 ly",
        "output": "2.394e-05 s"
    },
    {
        "instruction": "An aircraft of mass 120 kg executes a horizontal loop at a speed of 459 m/s with its wings banked at 70 degrees. What is the radius of the loop?",
        "input": "(v^2) / (g * tan((param * pi) / 180))",
        "output": "7668\nTo calculate the radius, we use the formula (v^2) / (g * tan((param * pi) / 180)), where v is the speed (459 m/s), g is the acceleration due to gravity (10 m/s^2), and param is the angle of banking (70 degrees)."
    },
    {
        "instruction": "A disc revolves with a speed of 20 rpm and has a radius of 1 m. Two coins are placed at 41 cm (coin-1) and 71 cm (coin-2) away from the center of the record. If the coefficient of friction between the coins and the record is 0.8, which of the coins will revolve with the record?",
        "input": "Centripetal acceleration (a) = (\u03c0 / 30) * rot_speed\nOptimal radius (r_opt) = ((\u03bc * g) / (w * w)) * 100",
        "output": "coin1 will revolve,coin2 will revolve"
    },
    {
        "instruction": "In a p-n junction diode, the current I can be expressed as I = I0*exp((e*V/2*k_b*T)-1), k_b = 8.6 * 10^(-5) eV/K. If for given diode I0 = 2086 x 10^(-15) A and T = 300 K, what will be dynamic resistance if the voltage across the diode is increased from 0.7 V to 2.2 V?\n",
        "input": "I=Io*exp((e*V/2*Kb*T)-1), R = V2/I2-I1",
        "output": "1.81e-25 ohm\nCalculate the resistance by dividing the increased voltage and the increase in current"
    },
    {
        "instruction": "Two lamps, one rated 96 W at 230 V, and the other 94 W at 240 V, which has more resistance?",
        "input": "",
        "output": "lamp2"
    },
    {
        "instruction": "A bullet of mass 100 kg and horizontal speed 98 m/s strikes a block of wood of mass 75 kg and instantly comes to rest with respect to the block. The block is suspended from the ceiling by a thin wire. Calculate the height to which the block rises.",
        "input": "h = (v^2) / (2 * g)",
        "output": "To calculate the height, we use the formula h = (v^2) / (2 * g), where h is the height, v is the velocity of the bullet after the collision, and g is the acceleration due to gravity (9.8 m/s^2)., this is the final answer 160.0"
    },
    {
        "instruction": "Earthquakes generate sound waves inside the earth, assuming the speed of transverse(S) wave is 1590 ms-1, speed of longitudinal(P) wave is 1800 ms-1, if the first P wave arrives 214 s before the first S wave to seismograph, at what distance does the earthquake occur?\n",
        "input": "Vs*Ts=Vp*Tp, L = Vp*Tp",
        "output": "2.92e+03 km\nTo determine the distance to the earthquake epicenter, we can use the difference in arrival times between the P wave and S wave at the seismograph.Using the formula for distance (d) based on wave speed and time: d = (P wave speed - S wave speed) * t"
    },
    {
        "instruction": "The transverse displacement of a string is given by y(x, t) = 0.09 sin 7\u03c0 /8 x cos (135\u03c0 t) where x, y are in m and t in s. The length of the string is 3 m and its mass is 0.1 kg,interpret this wave as a superimposition of two waves travelling in opposite direction, give  magnitude of speed of propagation of each wave?\n",
        "input": "speed = frequency*wavelength",
        "output": "29.5 ms-1\n"
    },
    {
        "instruction": "Calculate the frequency of a sound wave whose wavelength is 572 m and speed is 261976 m/s in a given medium ?\n",
        "input": "Wavelength = Speed / Frequency",
        "output": "458 hz\nTo calculate the frequency of a sound wave, we can use the formula: Frequency = Speed / Wavelength. In this case, the speed of the sound wave is 261976 m/s and the wavelength is 572 m. Substituting these values into the formula, we can calculate the frequency: Frequency = 261976 m/s / 572 m"
    },
    {
        "instruction": "A stone is thrown vertically upward with a velocity of 84611 m/s. What is the time taken by it to reach the maximum height?",
        "input": "time = initial_velocity / acceleration",
        "output": "The time taken by the stone to reach the maximum height is 8633.8 s."
    },
    {
        "instruction": "A circular coil of wire consisting of 95 turns, each of radius 319 cm carries a current of 15 A. What is the magnitude of the magnetic field B at the center of the coil?",
        "input": "B = (mu * n * i) / (2 * r)",
        "output": "To calculate the magnetic field B at the center of the coil, we use the following formula:\n\nB = (mu * n * i) / (2 * r)\n\nWhere,\n- B = Magnetic field at the center of the coil\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- n = Number of turns in the coil\n- i = Current flowing through the coil\n- r = Radius of the coil\n\nSubstituting the given values into the formula, we find that the magnitude of the magnetic field B is approximately 2.81e-04 tesla."
    },
    {
        "instruction": "You are riding an automobile of mass 11180 kg. The suspension sags 105 cm when the entire automobile is placed on it. Also, the amplitude of oscillation decreases by 19 percent during one complete oscillation. Estimate the value of the spring constant k?",
        "input": "",
        "output": "To estimate the value of the spring constant k, we use the formula (m * g) / (0.04 * x), where m is the mass of the automobile (11180 kg), g is the acceleration due to gravity (10 m/s^2), and x is the sag of the suspension (105 cm)., this is the final answer: 2.66e+04 newton-m-1"
    },
    {
        "instruction": "A solenoid of magnetic moment 1.41 J/T is kept in a uniform magnetic field of 0.59 T. What is the work done by an external torque to turn the magnet which is aligned at an angle of 89 degrees with the magnetic field to an angle of 101 degrees?",
        "input": "-m * b * (d1 - d2)",
        "output": "The work done by an external torque to turn the magnet aligned at an angle of 0.017452406437283376 degrees with the magnetic field to an angle of -0.1908089953765448 degrees can be calculated using the formula -m * b * (d1 - d2), where 'm' is the magnetic moment of the magnet, 'b' is the magnetic field strength, 'd1' is the initial angle, and 'd2' is the final angle. Substituting the given values, we have -(1.41) * 0.59 * (0.02 - -0.19)."
    },
    {
        "instruction": "Two long and parallel straight wires A and B carrying currents of 32 A and 33 A in the opposite direction are separated by a distance 100 cm. Estimate the force and its nature on the 22 cm section of wire B. (mu = 4 x pi x 10^(-7) TmA^-1)",
        "input": "Force = (mu * i1 * i2 * l) / (2 * pi * r)",
        "output": "To calculate the force and its nature, we use the following formula:\n\nForce = (mu * i1 * i2 * l) / (2 * pi * r)\n\nSubstituting the given values:\n- mu = 4 * pi * 10^(-7) TmA^-1\n- i1 = 32 A\n- i2 = 33 A\n- r = 100 cm\n- l = 22 cm\n\nAfter evaluating the formula, we find that the force on the 22 cm section of wire is approximately 4.65e-05 newtons and repulsive."
    },
    {
        "instruction": "A bike starting with an initial velocity of 616 m/s travels on a straight road at a constant rate of 61 m/s\u00b2 for 9 s. How far does the bike travel during this time?",
        "input": "initial velocity (u) = 616 m/s, acceleration (a) = 61 m/s\u00b2, time (t) = 9 s",
        "output": "8014.5 m \n\ndistance (s) = initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)\u00b2\ns = 616 * 9 + 0.5 * 61 * 9\u00b2\ns = 5544 + 2470.5\ns = 8014.5"
    },
    {
        "instruction": "A rigid bar of mass 13 kg is supported symmetrically by three wires each 12 m long. Those at each end are of material-1 and the middle one is of material-2. Find ratios of their diameters all have the same tension (Young's modulus of material-1 is 176 x 10^9 Nm-2, material-2 is 150 x 10^9 Nm-2).",
        "input": "diameter_ratio = sqrt(Y2 / Y1)",
        "output": "The ratio of their diameters is 0.92."
    },
    {
        "instruction": "An air bubble of volume 35 cm3 rises from the bottom of a lake 223 m deep at a temperature of 18 degree C. To what volume does it grow when it reaches the surface, which is at a temperature of 37 degree C.",
        "input": "(p1 * v * t2) / (t1 * p2)",
        "output": "852.1 cm3\np1 = initial pressure\np2 = final pressure\nV = volume\nt1 = initial temperature\nt2 = final temperature\nR = gas constant\nn = (2285400.0 * 35 * 10^5) / (8.314 * 291) - (100000 * 35 * 10^5) / (8.314 * 310)\nn = 3306185815.0 - 135798924.5\nn = 3170386890.5\nV = n * R * t2 / p2 = 817.1 cm3"
    },
    {
        "instruction": "A concave mirror produces 27 times diminished real image of an object at a distance of 1.46 cm from the mirror. At what distance is the object placed in front of the mirror?",
        "input": "Formula: u = v * n",
        "output": "To find the distance at which the object is placed in front of the mirror, we use the formula u = v * n, where u is the distance of the object from the mirror, v is the distance of the image from the mirror, and n is the magnification factor. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 39.4 cm in front of the mirror., this is the final The object is placed at a distance of 39.4 cm in front of the mirror."
    },
    {
        "instruction": "A convex lens produces a real image at a distance of 579 cm from it of a real object placed 37 cm in front of it. What is the magnification of the lens?",
        "input": "Formula: m = v / u",
        "output": "To calculate the magnification of the lens, we use the formula m = v / u, where m is the magnification, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for m. In this case, the magnification of the lens is 15.6., this is the final The magnification of the lens is 15.6."
    },
    {
        "instruction": "For an amplitude modulated wave, the maximum amplitude is found to be 23.47 V while the minimum amplitude is found to be 14.32 V. Determine the modulation index.\n",
        "input": "Modulation index = (a_max - a_min) / (a_max + a_min)",
        "output": "We know that the modulation index of an amplitude modulated wave is the ratio of the difference between a_max and a_min to the sum of a_max and a_min. The difference of a_max, a_min is equal to 23.47 - 14.32 = 9.15, and the sum of a_max, a_min is equal to 23.47 + 14.32 = 37.79. Hence, the modulation index is equal to 9.15 / 37.79 = 0.24\n"
    },
    {
        "instruction": "Calculate the speed of a sound wave whose frequency is 1880 hz and wavelength is 224 m in a given medium ?\n",
        "input": "Wavelength = Speed / Frequency",
        "output": "421120 m/s\nTo calculate the speed of a sound wave, we can use the formula: Speed = Frequency \u00d7 Wavelength. In this case, the frequency of the sound wave is 1880 Hz and the wavelength is 224 m. Substituting these values into the formula, we can calculate the speed: Speed = 1880 Hz \u00d7 224 m"
    },
    {
        "instruction": "An oxygen cylinder of volume 34 litre has an initial gauge pressure of 19 atmosphere and a temperature of 39 degree C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atmosphere and its temperature drops to 59 degree C. Estimate the number of moles of oxygen taken out of the cylinder.",
        "input": "n = (p1 * V) / (R * T1) - (p2 * V) / (R * T2)",
        "output": "11.4 mol  (p1 * V) / (R * T1) - (p2 * V) / (R * T2)"
    },
    {
        "instruction": "A steel rod 157 cm long is hinged at its middle. The fundamental frequency of longitudinal vibrations of the rod is given to be 1692 Hz. What is the speed of sound in steel?\n",
        "input": "speed of sound in steel = frequency*wavelength",
        "output": "5.3e+03 ms-1\nThe distance between two successive nodes is wavelength/2."
    },
    {
        "instruction": "A sound wave travels at a speed of 1305633.6 m/s, if it's wavelength is 48 m, will the sound wave be audible ? \n",
        "input": "frequency = wave speed / wavelength",
        "output": "not audible\nWhether a sound wave is audible or not depends on its frequency, not its wavelength. Audible sound waves have frequencies within the range of human hearing, which is typically between 20 Hz and 20,000 Hz. To determine if a sound wave is audible, we need to calculate its frequency using the wave speed and wavelength. The formula to calculate the frequency of a sound wave is: f = v / \u03bb, where f is the frequency, v is the wave speed, and \u03bb is the wavelength. Substituting the given values into the formula, we can calculate the frequency of the sound wave: f = 1305633.6 m/s / 48 m. Now, we can compare the calculated frequency to the audible frequency range (20 Hz to 20,000 Hz) to determine if the sound wave is audible or not."
    },
    {
        "instruction": "The equilibrium constant for a reaction is 446. Calculate the value of \u0394G^o, given R = 8.3 J/Kmol and T = 331.1.\n",
        "input": "\u0394G^o = -2.303RTlogK or -RTlnK",
        "output": "-38608.6\nTo calculate the standard Gibbs free energy change (\u0394G^o) for a reaction given the equilibrium constant (K), gas constant (R), and temperature (T), we can use the following equation: \u0394G^o = -R * T * ln(K) where ln represents the natural logarithm."
    },
    {
        "instruction": "A convex lens produces 29 times diminished real image of a 52.8 cm object placed in front of it. What is the height of the image formed by the lens?",
        "input": "Formula: hi = ho / n",
        "output": "To find the height of the image formed by the lens, we use the formula hi = ho / n, where hi is the height of the image, ho is the height of the object, and n is the magnification factor. By substituting the given values into the formula, we can solve for hi. In this case, the height of the image formed by the lens is 1.8 cm., this is the final The height of the image formed by the lens is 1.8 cm."
    },
    {
        "instruction": "The volume of 1607 g of a substance is 110 cm\u00b3. If the density of the liquid in which the substance is placed is 2 g/cm\u00b3, will the substance float or sink?",
        "input": "Density of Substance = 14.60909090909091 g/cm\u00b3, Density of Liquid = 2 g/cm\u00b3",
        "output": "The substance will sink."
    },
    {
        "instruction": "A circular coil of radius 3 cm consists of 30 turns and carries a current of 20 A. The coil is suspended vertically, and the normal to the plane of the coil makes an angle of 80 degrees with the direction of a uniform horizontal magnetic field of magnitude 13 tesla. What is the magnitude of the torque experienced by the coil.",
        "input": "Torque = n * b * i * A * sin(d)",
        "output": "To calculate the magnitude of the torque experienced by the coil, we use the following formula:\n\nTorque = n * b * i * A * sin(d)\n\nWhere,\n- n = Number of turns in the coil\n- b = Magnetic field\n- i = Current in the coil\n- A = Area of the coil\n- d = Angle between the normal to the coil and the magnetic field\n\nFor a square coil, the area (A) is equal to the square of the side length (l) of the coil. For a circular coil, the area (A) is equal to pi times the square of the radius (l) of the coil.\n\nSubstituting the given values into the formula and evaluating it, we find that the magnitude of the torque experienced by the coil is approximately 21.7 newton-m."
    },
    {
        "instruction": "A heating element using nichrome connected to a 238 V supply draws an initial current of 837 mA which settles after a few seconds to a steady value of 715 mA. What is the steady temperature of the heating element if room temperature is 27 degree C (temp coeff of nichrome is 1.70 x 10^(-4) degree C-1)?",
        "input": "T = ((R2 - R1) / (R1 * temp_coeff)) + T_room",
        "output": "1031 degree centigrade\n\nTo calculate the steady temperature of the heating element, use the formula: T = ((R2 - R1) / (R1 * temp_coeff)) + T_room, where R2 is the resistance with steady current, R1 is the resistance with initial current, temp_coeff is the temperature coefficient, and T_room is the room temperature."
    },
    {
        "instruction": "In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 292 x 10^8 Hz and amplitude 1562 V/m. What is the amplitude of the oscillating magnetic field?",
        "input": "A = 1562 V/m",
        "output": "5.21e-06 tesla\n\nThe amplitude of the oscillating magnetic field can be calculated by dividing the electric field amplitude by the speed of light."
    },
    {
        "instruction": "A solid sphere and a solid disk roll down two different inclined planes of heights 4 and 17 and with angles of inclination of 10 and 67, which one reaches the bottom with more speed?",
        "input": "speed = height / (1 + k)",
        "output": "To compare the speeds, we use the following formula:\n\nspeed = height / (1 + k)\n\nSubstituting the given values into the formula, we find that:\n\nThe solid disk reaches the bottom with more speed."
    },
    {
        "instruction": "A steady current of 4 A flows through a conductor, then calculate the time taken for 50883658381721498814 electrons to pass through any cross section of the conductor?",
        "input": "t = (n * e) / I",
        "output": "2.0 s\n\nThe time taken for the electrons to pass through any cross section of the conductor can be calculated using the formula: t = (n * e) / I, where n is the number of electrons, e is the charge of an electron, and I is the current."
    },
    {
        "instruction": "What is the gravitational field at a point P on the surface of the uniform solid sphere of radius 419 m and mass 482 kg?",
        "input": "Gravitational Field (g) = cal3(482, 419) N/kg",
        "output": "The gravitational field at a point P on the surface of the uniform solid sphere of radius 419 m and mass 482 kg is given by the formula g = (-G * m) / (r^2), where G is the gravitational constant, m is the mass, and r is the distance. Plugging in the values, we get g = -1.83e-13 N/kg."
    },
    {
        "instruction": "Find the radius of curvature of a convex mirror whose focal length is 1517.83 cm.",
        "input": "Formula: R = 2 * f",
        "output": "To find the radius of curvature of a convex mirror, we use the formula R = 2 * f, where R is the radius of curvature and f is the focal length. By substituting the given value of f into the formula, we can solve for R. In this case, the radius of curvature is 3035.7 cm., this is the final 3035.7"
    },
    {
        "instruction": "A convex mirror produces 24 times diminished real image of an object at a distance of 18 cm from the mirror. At what distance is the object placed in front of the mirror?",
        "input": "Formula: u = v * n",
        "output": "To find the distance at which the object is placed in front of the mirror, we use the formula u = v * n, where u is the distance of the object from the mirror, v is the distance of the image from the mirror, and n is the magnification factor. By substituting the given values into the formula, we can calculate u. In this case, the object is placed at a distance of 432 cm in front of the mirror., this is the final The object is placed at a distance of 432 cm in front of the mirror."
    },
    {
        "instruction": "An object is placed at 315 cm in front of a convex lens of focal length 364 cm. Find at what distance image is formed and its nature.",
        "input": "Formula: 1/f = 1/v - 1/u for convex lens.",
        "output": "To find the distance of the image formed, we use the formula for convex lenses: 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for v. In this case, the image is virtual and located at a distance of 2340.0 cm., this is the final The image is formed at 2340.0 cm and it is virtual."
    },
    {
        "instruction": "A parallel plate capacitor made of circular plates of radius r = 127 cm has a capacitance C = 178 pF. The capacitor is connected to a 230 V ac supply with an angular frequency of 700 rad/s. Determine the amplitude of B at a point 2 cm from the axis between the plates?",
        "input": "d = 2 cm, r = 127 cm, I = 2.87e-05 ampere",
        "output": "1.01e-13 tesla\n\nThe amplitude of the magnetic field at a point between the plates can be calculated using the formula: B = (\u03bc\u2080dI\u2080) / (r\u00b2), where \u03bc\u2080 is the permeability of free space, d is the distance from the axis, I\u2080 is the rms current, and r is the radius of the plates."
    },
    {
        "instruction": "The coefficient of volume expansion of copper is 5.1e-05 K^-1. What is the change in its volume 43 m^3 for a rise in temperature from 92 degree C to 441 degree C?",
        "input": "Change in volume = d1 * a * (t2 - t1)",
        "output": "To find the change in volume, we use the following formula:\n\nChange in volume = d1 * a * (t2 - t1)\n\nSubstituting the given values into the formula, we find that the change in volume is approximately 0.77 m^3."
    },
    {
        "instruction": "In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are 65 ms-1 and 36 ms-1. What is the lift on the wing if its area is 34700 cm2? (Take the density of air to be 1.3 kgm-3)",
        "input": "0.5 * 1.3 * (65**2 - 36**2) * (34700 / 10000)",
        "output": "The lift on the wing is 6606.3595000000005 newton."
    },
    {
        "instruction": "A short bar magnet of magnetic moment 3.18 J/T is placed in a uniform magnetic field of 6.61 T. If the magnet is free to rotate in the plane of the field, what is the potential energy of the magnet at a position making an angle of 93 degrees with the magnetic field?",
        "input": "-m * b * -0.05",
        "output": "The potential energy of the magnet at a position making an angle of -0.05233595624294362 degrees with the magnetic field can be calculated using the formula -m * b * cos(d), where 'm' is the magnetic moment of the bar magnet, 'b' is the magnetic field strength, and 'd' is the angle. Substituting the given values, we have -(3.18) * 6.61 * -0.05 = 1.10e+00 joule."
    },
    {
        "instruction": "What is the gravitational potential at a point P on the surface of the spherical shell of radius 408 m and having -2.92e+02 C charge distributed uniformly on it.\n",
        "input": "To calculate the gravitational potential at a point on the surface of a uniformly charged spherical shell, we use the formula:\n\nV = (k * Q) / r\n\nwhere V is the gravitational potential, k is the electrostatic constant (9 * 10^9 Nm^2/C^2), Q is the charge, and r is the distance from the center of the shell.",
        "output": "-6.44e+09 joule/coulomb\n"
    },
    {
        "instruction": "Two circular coils X and Y of radii 36 cm and 25 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil A has 4 turns and carries a current of 14 A, Coil B has 19 turns and carries a current of 12 A. The sense of current in X is anti-clockwise direction and in Y is clockwise direction. From an observer looking at the coils facing west, give the magnitude and direction of the net magnetic field due to the coils at the center.",
        "input": "Net magnetic field = |b1 - b2|",
        "output": "To calculate the net magnetic field, we use the following formula:\n\nNet magnetic field = |b1 - b2|\n\nWhere,\n- b1 = Magnetic field due to coil X\n- b2 = Magnetic field due to coil Y\n\nWe calculate the magnetic field for each coil using the formula:\n- Magnetic field due to coil X = (mu * n1 * i1) / (2 * r1)\n- Magnetic field due to coil Y = (mu * n2 * i2) / (2 * r2)\n\nSubstituting the given values and evaluating the formula, we find that the magnitude of the net magnetic field is approximately 4.75e-04 tesla and towards west."
    },
    {
        "instruction": "In a uniform electric field of 8887 N/C, what is the flux through a square of 66 cm, whose plane is parallel to the yz-plane?\n",
        "input": "Flux = Electric field * Area",
        "output": "To calculate the flux through the square, we use the formula:\nFlux = Electric field * Area\nGiven electric field = 8887 N/C, area = 4356 cm\u00b2,\nFlux = 3.87e+03 N\u00b7m\u00b2/C\n"
    },
    {
        "instruction": "In a double-slit experiment the angular width of a fringe is found to be 1.0 degrees on a screen placed 6 m away. The wavelength of light used is 11 nm. What will be the angular width of the fringe if the entire experimental apparatus is immersed in liquid of refractive index 1.02.\n",
        "input": "refractive index = angular width before immersing in water/angular width after immersing in water",
        "output": "9.80e-01 degrees\nTo calculate the angular width of a fringe when the entire experimental apparatus is immersed in a liquid of refractive index (\u03bc), we need to consider the effect of the refractive index on the wavelength of light.we can calculate the angular width of the fringe in the liquid (\u03b82') using the formula: \u03b82' = sin^(-1)(\u03bb' / d), where d is the distance to the screen (D) in meters."
    },
    {
        "instruction": "A wheel reaches an angular position of 497 rad when applied with a constant angular acceleration of 10 rad/s\u00b2 for 5 seconds. What is its initial angular velocity?",
        "input": "initial_angular_velocity = (angular_position - (0.5 * angular_acceleration * time^2)) / time",
        "output": "To calculate the initial angular velocity, we use the following formula:\n\ninitial_angular_velocity = (angular_position - (0.5 * angular_acceleration * time^2)) / time\n\nSubstituting the given values into the formula, we find that the initial angular velocity is approximately 74.4 rad/s."
    },
    {
        "instruction": "Compute the bulk modulus of a material from the following data: Initial volume = 226 litre, Pressure increase = 100 atm (1 atm = 1.013 x 10^5 Pa), volume increased = 820 ml.",
        "input": "bulk modulus = (pressure_increase * 1.013 * (10 ** 8) * initial_volume) / (final_volume - initial_volume)",
        "output": "The bulk modulus of the material is 2.79e+09."
    },
    {
        "instruction": "Torque of 920 Nm is transmitted to an engine at a power of 374 W. What is the angular speed of the rotor?",
        "input": "Angular Speed = Power / Torque",
        "output": "Angular Speed = 374 W / 920 Nm\n\nTo calculate the angular speed of the rotor, we use the following formula:\n\nAngular Speed = Power / Torque\n\nSubstituting the values:\n\nPower = 374 W\nTorque = 920 Nm\n\nWe find that the angular speed of the rotor is 0.4 rad/s."
    },
    {
        "instruction": "A body is dropped from the top of a building of height 523 m with an initial velocity of 40 m/s under gravity. After what time does it reach the ground?",
        "input": "height (h) = 523 m, initial velocity (u) = 40 m/s",
        "output": "time (t) = (-(2 * initial velocity (u)) + \u221a((4 * initial velocity (u)\u00b2) + (8 * acceleration (a) * height (s)))) / (2 * acceleration (a))\nt = (-(2 * 40) + \u221a((4 * 40\u00b2) + (8 * 9.8 * 523))) / (2 * 9.8)\nt = (-(2 * 40) + \u221a(6400 + 41003.200000000004)) / 19.6\nt = (-(2 * 40) + \u221a(47403.200000000004)) / 19.6\nt = (-(2 * 40) + \u221a(47403.200000000004)) / 19.6\nt = (-(2 * 40) + \u221a(47403.200000000004)) / 19.6\nt = (-(2 * 40) + \u221a(47403.200000000004)) / 19.6\nt = (-(2 * 40) + \u221a(47403.200000000004)) / 19.6\nt = (-(2 * 40) + \u221a(47403.200000000004)) / 19.6\nt = (-(2 * 40) + \u221a(47403.200000000004)) / 19.6\nt = (-(2 * 40) + \u221a(47403.200000000004)) / 19.6\nt = 7.0"
    },
    {
        "instruction": "Light enters from a material-1 having refractive index 1.8 to material-2 having refractive index 5.6. If the speed of light in material-1 is 227800000 m/s, what is the speed of light in material-2?",
        "input": "Speed of Light in a Material (v) = (n1 * c) / n2",
        "output": "The speed of light in a material can be calculated using the formula v = (n1 * c) / n2, where v is the speed of light in the material, n1 is the refractive index of material-1, c is the speed of light in vacuum, and n2 is the refractive index of material-2., this is the final 73221428.6 m/s"
    },
    {
        "instruction": "A long straight wire in the horizontal plane carries a current of of 462 A in west to east direction. What is the magnitude and direction of the magnetic field B at a point 113 cm south of the wire. (mu = 4 x pi x 10-7 TmA-1)\n",
        "input": "B = (mu * i) / (2 * pi * r)",
        "output": "To calculate the magnitude and direction of the magnetic field B, we use the following formula:\n\nB = (mu * i) / (2 * pi * r)\n\nWhere,\n- B = Magnetic field\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- i = Current flowing through the wire\n- r = Distance from the wire\n\nSubstituting the given values into the formula, we find that the magnitude and direction of the magnetic field B is approximately 8.2e-05 tesla vertically downwards\n."
    },
    {
        "instruction": "What is the gravitational potential at a point P at a distance of 302 m from the center of the spherical shell of radius 382 m and mass 299 kg?",
        "input": "Gravitational Potential (V) = cal1(299, 302, 382) joule/kg",
        "output": "The gravitational potential at a point P at a distance of 302 m from the center of the spherical shell of radius 382 m and mass 299 kg is given by the formula V = (-G * m) / R, where G is the gravitational constant, m is the mass, and R is the distance. Plugging in the values, we get V = -5.22e-11 joule/kg."
    },
    {
        "instruction": "A stone of mass 354 g dropped from the top of a tower of height 1671 m high splashes into the water of a pond near the base of the tower. When is the splash heard at the top given that the speed of sound in air is 340 ms-1 ? (g = 9.8 ms-2 )\n",
        "input": "Height = Initial Speed + 1/2*g*time^2, Total time = t1+t2",
        "output": "23.38 s\nUse the equation of motion: Height = Initial Speed + 1/2*g*time^2, to calculate the time of splash heard."
    },
    {
        "instruction": "Calculate root mean square velocity of a gas molecule having molar mass of 239 g/mol at 136 degree C. (R = 8.31 J/molK)",
        "input": "math.sqrt((3 * r * t1 * 1000) / m)",
        "output": "206.5493548362318 m/s\n The formula used is: math.sqrt((3 * r * t1 * 1000) / m)"
    },
    {
        "instruction": "A concave mirror produces 47 times magnified virtual image of an object at a distance of 5728 cm from the mirror. At what distance is the object placed in front of the mirror?",
        "input": "Formula: u = v * n",
        "output": "To find the distance at which the object is placed in front of the mirror, we use the formula u = v * n, where u is the distance of the object from the mirror, v is the distance of the image from the mirror, and n is the magnification factor. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 269216 cm in front of the mirror., this is the final The object is placed at a distance of 269216 cm in front of the mirror."
    },
    {
        "instruction": "If a car attains a velocity of 256 m/s by applying a constant acceleration of 27 m/s\u00b2 for 4 s, then what is the initial velocity of the car?",
        "input": "initial_velocity = final_velocity - (acceleration * time)",
        "output": "The initial velocity of the car is 148 m/s."
    },
    {
        "instruction": "A rope of negligible mass is wound round a solid cylinder of mass 6 kg and radius 36 cm. What is the angular acceleration of the solid cylinder if the rope is pulled with a force of 85 N? Assume that there is no slipping.",
        "input": "Acceleration = Force / (k * mass * radius)",
        "output": "Acceleration = 85 N / (0.5 * 6 kg * 36 cm)\n\nTo calculate the angular acceleration of the solid cylinder, we use the following formula:\n\nAcceleration = Force / (k * mass * radius)\n\nSubstituting the values:\n\nForce = 85 N\nk = 0.5\nMass = 6 kg\nRadius = 36 cm\n\nWe find that the angular acceleration of the solid cylinder is approximately 78.7 rad/s\u00b2."
    },
    {
        "instruction": "On an unknown scale, the temperature of the melting point and boiling point of water is 63 degrees and 175 degrees respectively. If the temperature on the Kelvin scale is 318 degrees Kelvin, what is the temperature shown on that scale?",
        "input": "Temperature on the unknown scale = (((t2 - t1) * (t - ta)) / (tb - ta)) + t1",
        "output": "To find the temperature on the unknown scale, we use the following formula:\n\nTemperature on the unknown scale = (((t2 - t1) * (t - ta)) / (tb - ta)) + t1\n\nSubstituting the given values into the formula, we find that the temperature on the unknown scale is approximately 113.4."
    },
    {
        "instruction": "How much should the pressure of 258 ml of water be changed to compress it by 73.7%, assuming a bulk modulus of elasticity of water to be 2.2 x 10^9 N/m^2?",
        "input": "pressure_change = (bulk_modulus * percent) / 100",
        "output": "The pressure of 258 ml of water needs to be changed by 1.6e+09 Pa to compress it by 73.7%. The formula to calculate the pressure change is:\n\npressure_change = (bulk_modulus * percent) / 100"
    },
    {
        "instruction": "15 identical hollow cylindrical columns of mild steel support a big structure of mass 34350 kg. The inner and outer radii of each column are 25 cm and 35 cm respectively. Calculate the compressional strain of each column.",
        "input": "strain = F / (A * Y)",
        "output": "The compressional strain of each column is 6.0e-07."
    },
    {
        "instruction": "A convex lens produces 69 times magnified real image of a 81.63 cm object placed in front of it. What is the height of the image formed by the lens?",
        "input": "Formula: hi = n * ho",
        "output": "To find the height of the image formed by the lens, we use the formula hi = n * ho, where hi is the height of the image, n is the magnification factor, and ho is the height of the object. By substituting the given values into the formula, we can solve for hi. In this case, the height of the image formed by the lens is 5632.5 cm., this is the final The height of the image formed by the lens is 5632.5 cm."
    },
    {
        "instruction": "6 identical hollow cylindrical columns of mild steel support a big structure of mass 32460 kg. The inner and outer radii of each column are 20 cm and 51 cm respectively. Calculate the compressional strain of each column.",
        "input": "strain = F / (A * Y)",
        "output": "The compressional strain of each column is 3.8e-07."
    },
    {
        "instruction": "Light enters from a material-1 having refractive index 7.1 to material-2. If the speed of light in material-1 and material-2 is 187000000 m/s and 52000000 m/s respectively, what is the refractive index of material-2?",
        "input": "Speed of Light in a Material (v) = (n1 * c) / n2",
        "output": "The speed of light in a material can be calculated using the formula v = (n1 * c) / n2, where v is the speed of light in the material, n1 is the refractive index of material-1, c is the speed of light in vacuum, and n2 is the refractive index of material-2., this is the final 25.5"
    },
    {
        "instruction": "If a diatomic gas of 10 moles at 26 pas is isothermally changed to pressure 37 pas at 31 K, then what is the work done.\n",
        "input": "Work Done = n*R*T*ln(P1/P2)",
        "output": "908.9 joules\nTo calculate the work done during an isothermal expansion of a diatomic gas, we can use the following equation: Work done = n * R * T * ln(P1/P2), where n is the number of moles of the gas, R is the ideal gas constant (approximately 8.314 J/(mol\u00b7K)), T is the temperature in Kelvin, P1 is the initial pressure, and P2 is the final pressure."
    },
    {
        "instruction": "A convex mirror produces a real image at a distance of 14 cm from it of a real object having a height of 81 cm and placed 74 cm in front of it. What is the height of the image?",
        "input": "Formula: m = v / u = hi / ho",
        "output": "To find the height of the image, we use the formula m = v / u = hi / ho, where m is the magnification, v is the distance of the image from the mirror, u is the distance of the object from the mirror, hi is the height of the image, and ho is the height of the object. By rearranging the formula, we can calculate hi as hi = (v * ho) / u. By substituting the given values into the formula, we find that the height of the image is 15.3 cm., this is the final The height of the image is 15.3 cm."
    },
    {
        "instruction": "An image is formed by a concave lens of focal length 744 cm at a distance of 160 cm behind it. Find at what distance object is placed in front of lens.",
        "input": "Formula: 1/f = 1/v - 1/u for concave lens.",
        "output": "This is the answer The object is placed at 204 cm in front of the lens., formula used is : Formula: 1/f = 1/v - 1/u for concave lens."
    },
    {
        "instruction": "A hollow cylinder of mass 1220 kg has a radius of 87 m. What is the moment of inertia with respect to its symmetric axis?",
        "input": "Moment of Inertia = (Constant) * mass * radius^2",
        "output": "The moment of inertia with respect to its symmetric axis is approximately 9234180 kgm^2.\n\nMoment of Inertia = (Constant) * mass * radius^2\n\nConstant = 1\nmass = 1220 kg\nradius = 87 m"
    },
    {
        "instruction": "A short bar magnet placed with its axis at 28 degrees with a uniform external magnetic field of 0.04 T experiences a torque of magnitude equal to 0.182 J. What is the magnitude of the magnetic moment of the bar magnet?",
        "input": "t / (b * sin(d*pi/180))",
        "output": "If 'b' is the magnetic field strength, 't' is the torque due to that magnetic moment, 'd' is the angle between the axis of the magnet and the magnetic field, and 'm' is the magnetic moment, then t = m * b * sin(d). Solving for 'm', we have m = t / (b * sin(d)) = 0.182 / (0.04 * 0.47)."
    },
    {
        "instruction": "A wheel starting with an initial angular velocity of 75 rad/s is applied with a constant angular acceleration of 10 rad/s\u00b2. What is the time taken to reach an angular position of 865 rad?",
        "input": "time = (-(2 * initial_angular_velocity) + sqrt((4 * initial_angular_velocity^2) + (8 * angular_acceleration * angular_position))) / (2 * angular_acceleration)",
        "output": "To calculate the time, we use the following formula:\n\ntime = (-(2 * initial_angular_velocity) + sqrt((4 * initial_angular_velocity^2) + (8 * angular_acceleration * angular_position))) / (2 * angular_acceleration)\n\nSubstituting the given values into the formula, we find that the time is approximately 7.6 seconds."
    },
    {
        "instruction": "A 3m long tube open at one end, with a movable piston at the other end, shows resonance with a fixed frequency source (a turning fork of frequency 725 Hz) when the tube length is 63 cm or 197 cm. Estimate the speed of sound in air.\n",
        "input": "wavelength = 4*length of tube, speed of sound = frequency*wavelength",
        "output": "1.83e+03 ms-1\nSince the given pipe is attached with a piston at one end, it will behave as a pipe with one end closed and the other end open. Such a system produces odd harmonics."
    },
    {
        "instruction": "A sound produces 1952 crests and 1952 troughs in 30 seconds. When the first trough is produced, the first crest is 161 m away from the source, then calculate the time period ?\n",
        "input": "Wavelength = Speed*Time Period, ",
        "output": "15.4 ms\nTo calculate the speed of sound, we need to determine the distance traveled by a crest or trough in the given time interval. In 30 seconds, 1952 crests and 1952 troughs are produced. This means that one complete cycle of the wave (a crest and a trough) occurs 1952 times in 30 seconds. Therefore, the time taken for one complete cycle (T) can be calculated as: T = 30 s / 1952 cycles. The distance traveled by one complete cycle (wavelength, \u03bb) is given by the formula: \u03bb = speed * T, where speed is the speed of sound. Since the first crest is 161 m away from the source, the distance traveled by a complete cycle (\u03bb) can be expressed as: \u03bb = 161 m + 161 m = 2 * 161 m. Substituting the value of \u03bb and T into the equation, we can calculate the speed of sound: speed = \u03bb / T = (2 * 161 m) / (30 s / 1952 cycles). Calculating this expression will give us the speed of sound."
    },
    {
        "instruction": "Two objects of masses 7 g and 3 g are moving along the same line and direction with velocities of 10 m/s and 20 m/s respectively. They collide and after the collision, the first object moves at a velocity of 27 m/s. Determine the velocity of the second object.",
        "input": "v2 = ((m1 * u1) + (m2 * u2) - (m1 * v1)) / m2",
        "output": "To find the velocity of the second object (v2), we use the formula:\n\nv2 = ((m1 * u1) + (m2 * u2) - (m1 * v1)) / m2\n\nSubstituting the given values, we have:\n\nv2 = ((7 * 10) + (3 * 20) - (7 * 27)) / 3\n\nSimplifying the expression gives us v2 = -19.7 m/s."
    },
    {
        "instruction": "If a wheel of radius 973 m has an angular velocity of 147 rad/s, what is the velocity of a point at the circumference of the wheel?",
        "input": "velocity_at_circumference = angular_velocity * radius",
        "output": "To calculate the velocity at the circumference, we use the following formula:\n\nvelocity_at_circumference = angular_velocity * radius\n\nSubstituting the given values into the formula, we find that the velocity at the circumference is approximately 143031 m/s."
    },
    {
        "instruction": "Suppose that the electric field amplitude of an electromagnetic wave is E0 = 1163 N/C and that its frequency is v = 211 MHz. Find an expression for E?",
        "input": "E0 = 1163 N/C, k = 4.42e+00 rad/m, w = 1.33e+09 rad/s",
        "output": "1163sin[4.42e+00x-1.33e+09t]\n\nThe expression for the electric field (E) of an electromagnetic wave can be written as E = E0sin(kx - wt)."
    },
    {
        "instruction": "A car moving along a straight highway with a speed of 262 ms-1 is brought to a stop within a distance of 8406 m. What is the acceleration of the car (assumed uniform), and how long does it take for the car to stop?",
        "input": "a = -v^2 / s, t = v / a",
        "output": "The acceleration of the car is 8.2 ms-2 and it takes 32.1 seconds to stop."
    },
    {
        "instruction": "A force is applied on a body of mass 479 kg placed on a smooth surface resulting in acceleration of 356 m/s^2, then what is the force applied?",
        "input": "F = m * a",
        "output": "170524\nTo calculate the force, we use the formula F = m * a, where F is the force, m is the mass (479 kg), and a is the acceleration (356 m/s^2)."
    },
    {
        "instruction": "A bike travels a distance of 743 m on a straight road at a constant rate of 70 m/s\u00b2 for 3 s. What is the initial velocity of the bike?",
        "input": "distance (s) = 743 m, acceleration (a) = 70 m/s\u00b2, time (t) = 3 s",
        "output": "distance (s) = initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)\u00b2\ns = u * 3 + 0.5 * 70 * 3\u00b2\ns = 3u + 315.0\ns = 3u + 315\ns = 743\n\ns - 315 = 3u\n142.7 = 428 / 3\n142.7 = 142.7"
    },
    {
        "instruction": "Two sitar strings A and B playing the note \u2018Ga\u2019 are slightly out of tune and produce beats of frequency 53 Hz. The tension in the string A is slightly reduced and the beat frequency is found to be 23 Hz. If the original frequency of A is 392 Hz, what is the frequency of B?\n",
        "input": "Beat frequency = |f1+-f2|",
        "output": "339 hertz\nFrequency decreases with a decrease in the tension of a string.\nThis is because frequency is directly proportional to the square root of tension."
    },
    {
        "instruction": "For the travelling harmonic wave y(x, t) = 36 cos 2\u03c0 (43t \u2013 0.006x + 0.35) where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of 2\u03bb/5 ?\n",
        "input": "Phase difference = (2pi/wavelength)* Path difference",
        "output": "0.8 \u03c0 rad\nTo calculate the phase difference between two points in a traveling harmonic wave, we need to compare the phase angles of the wave at those points.In the given wave equation, the phase angle is represented by the term inside the cosine function, i.e., 2\u03c0(wt - kx + 0.35), where w represents the angular frequency and k represents the wave number.Let's assume the two points are at x1 and x2, separated by a distance \u0394x = x2 - x1. The phase difference between the oscillatory motion of these two points can be calculated using the equation: Phase difference = 2\u03c0(k\u0394x)"
    },
    {
        "instruction": "A concave lens produces a real image of height 63 cm at a distance of 62 cm from it of a real object placed 87 cm in front of it. What is the height of the object?",
        "input": "Formula: ho = (hi * u) / v",
        "output": "To find the height of the object, we use the formula ho = (hi * u) / v, where ho is the height of the object, hi is the height of the image, u is the distance of the object from the lens, and v is the distance of the image from the lens. By substituting the given values into the formula, we can solve for ho. In this case, the height of the object is 88.4 cm., this is the final The height of the object is 88.4 cm."
    },
    {
        "instruction": "The coefficient of volume expansion of glycerine is 0.0004900000000000001 K^-1. What is the change in its volume 74 m^3 for a rise in temperature from 75 degree C to 296 degree C?",
        "input": "Change in volume = d1 * a * (t2 - t1)",
        "output": "To find the change in volume, we use the following formula:\n\nChange in volume = d1 * a * (t2 - t1)\n\nSubstituting the given values into the formula, we find that the change in volume is approximately 8.01 m^3."
    },
    {
        "instruction": "A large steel wheel is to be fitted onto a shaft of the same material. At 83 degree C, the outer diameter of the shaft is 159 cm and the diameter of the central hole in the wheel is 158.986 cm. The shaft is cooled using 'dry ice'. At what temperature of the shaft does the wheel slip on the shaft? Assume the coefficient of linear expansion of the steel to be constant over the required temperature range \u03b1steel = 1.20 x 10-5K-1.",
        "input": "Required temperature = t1 + ((d2 - d1) / (\u03b1 * d1))",
        "output": "To calculate the required temperature, we use the following formula:\n\nRequired temperature = t1 + ((d2 - d1) / (\u03b1 * d1))\n\nSubstituting the given values into the formula, we find that the temperature is approximately 75.7 degree C."
    },
    {
        "instruction": "A meter stick is balanced on a knife edge at its center. When two coins, each of mass 22 g and 37 g respectively, are put at the 31 mark and 58 mark respectively, the stick is found to be balanced at 48 cm. What is the mass of the meter stick?",
        "input": "Mass = (Right Side - Left Side) / Distance",
        "output": "The mass of the meter stick is approximately 2.0 g.\nLeft Side = m1 * (t3 - t1) = 22 * (48 - 31)\nRight Side = m2 * (t2 - t3) = 37 * (58 - 48)"
    },
    {
        "instruction": "A concave lens produces 48 times diminished real image of height 34.43 cm of an object placed in front of it. What is the height of the object?",
        "input": "Formula: ho = n * hi",
        "output": "To find the height of the object, we use the formula ho = n * hi, where ho is the height of the object, hi is the height of the image, and n is the magnification factor. By substituting the given values into the formula, we can solve for ho. In this case, the height of the object is 1652.6 cm., this is the final The height of the object is 1652.6 cm."
    },
    {
        "instruction": "A polythene is rubbed with wool is found to have a negative charge of 707098 x 10^(-12) C. Is there a transfer of mass from wool to polythene?\n",
        "input": "Mass = (number of electrons) * (mass of one electron)",
        "output": "To determine if there is a transfer of mass, we consider the mass associated with the number of electrons transferred:\nMass = (number of electrons) * (mass of one electron)\nGiven number of electrons = 4.419e+12, mass of one electron = 9.1 x 10^(-31) kg,\nMass = 4.022e-18 kg of mass is transferred\n"
    },
    {
        "instruction": "Two bodies A and B of masses 1 kg and 16 kg are in contact with each other rest on a table. The coefficient of friction between the bodies and the table is 0.9. A force of 32 N is applied horizontally to A. Then what is the value of acceleration.",
        "input": "",
        "output": "0 ms^-2"
    },
    {
        "instruction": "If a car attains a velocity of 1676 m/s by applying a constant acceleration of 26 m/s\u00b2 for 38 s, then what is the initial velocity of the car?",
        "input": "initial_velocity = final_velocity - (acceleration * time)",
        "output": "The initial velocity of the car is 688 m/s."
    },
    {
        "instruction": "A batsman deflects a ball by an angle of 55 degrees without changing its initial speed, which is equal to 102 m/s. What is the impulse imparted to the ball? (The mass of the ball is 112 g)",
        "input": "Impulse calculation",
        "output": "13.1\nThe impulse imparted to the ball can be calculated using the formula (2 * mass * velocity * cos(angle)) / 1000, where the mass is 112 g, the velocity is 102 m/s, and the angle is 55 degrees. The result is 13.1 kg\u00b7m/s, perpendicular to the point of impact on the bat."
    },
    {
        "instruction": "A coil of inductance 0.68 H and resistance 89 ohm is connected to a 232 V, 20 Hz ac supply. What is the time lag between voltage maximum and current maximum?",
        "input": "Time_lag = atan((f * L * 2 * pi) / R) / (2 * pi * f)",
        "output": "6.09e-03 s"
    },
    {
        "instruction": "Two bodies A and B of masses 15 kg and 4 kg are in contact with each other rest on a table against a rigid wall (such that B is attached to the wall). The coefficient of friction between the bodies and the table is 0.64. A force of 69 N is applied horizontally to A. Then what is the value of action-reaction forces between A and B.",
        "input": "",
        "output": "69 newton"
    },
    {
        "instruction": "A spring balance has a scale that reads from 0 to 59 kg. The length of the scale is 99 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 295 ms. What is the weight of the body?",
        "input": "Formula: w = (t^2 * k) / (4 * \u03c0^2), where w is the weight of the body, t is the period of oscillation (295 ms), and k is the spring constant given by (m * g) / (l * 0.01), where m is the reading on the scale (59 kg), g is the acceleration due to gravity (9.8 m/s^2), and l is the length of the scale (99 cm).",
        "output": "To calculate the weight of the body, we use the formula w = (t^2 * k) / (4 * \u03c0^2), where w is the weight, t is the period of oscillation (295 ms), and k is the spring constant given by (m * g) / (l * 0.01). We substitute the given values and solve for w., this is the final answer 1.26e+01 newton"
    },
    {
        "instruction": "A concave lens produces a real image of height 88 cm at a distance of 5 cm from it of a real object placed 40 cm in front of it. What is the height of the object?",
        "input": "Formula: ho = (hi * u) / v",
        "output": "To find the height of the object, we use the formula ho = (hi * u) / v, where ho is the height of the object, hi is the height of the image, u is the distance of the object from the lens, and v is the distance of the image from the lens. By substituting the given values into the formula, we can solve for ho. In this case, the height of the object is 704.0 cm., this is the final The height of the object is 704.0 cm."
    },
    {
        "instruction": "In Mullikan\u2019s oil drop experiment, what is the viscous force on the drop of radius 483 x 10^(-6) m and density 2872 kg m-3 at terminal speed?",
        "input": "(2 / (9 * 1.8 * (10 ** -5))) * (483 ** 2 * 2872 * 9.8 * (10 ** -12))",
        "output": "The viscous force on the drop is 8.11e+01 newton."
    },
    {
        "instruction": "A wheel starting with an initial angular velocity of 77 rad/s accelerates and reaches a final velocity of 157 rad/s when the angular position is 53 rad. What is its angular acceleration?",
        "input": "angular_acceleration = ((final_angular_velocity^2 - initial_angular_velocity^2) / (2 * angular_position))",
        "output": "To calculate the angular acceleration, we use the following formula:\n\nangular_acceleration = ((final_angular_velocity^2 - initial_angular_velocity^2) / (2 * angular_position))\n\nSubstituting the given values into the formula, we find that the angular acceleration is approximately 176.6 rad/s\u00b2."
    },
    {
        "instruction": "A circular coil of radius 25 cm and 2 turns is rotated about its vertical diameter with an angular speed of 67 rad/s in a uniform horizontal magnetic field of magnitude 8.2 T. Obtain the maximum and average emf induced in the coil. If a coil forms a closed loop of resistance 10 ohm, what is the maximum current in the coil and average power loss due to joule heating?\n",
        "input": "EMF = n * w * b * A, I = EMF / R, P = (EMF * I) / 2",
        "output": "maximum emf: 2.16e+02 volt, average emf: 0 volts, maximum current: 2.16e+01 amp, average power loss: 2.33e+03 joule\n\n\nThe maximum emf induced in the coil can be calculated using the formula EMF = n * w * b * A, where n is the number of turns, w is the angular speed, b is the magnetic field magnitude, and A is the area of the coil.\nThe maximum current in the coil can be calculated using the formula I = EMF / R, where R is the resistance of the coil.\nThe average power loss due to joule heating can be calculated using the formula P = (EMF * I) / 2."
    },
    {
        "instruction": "Obtain the Q-value of a series LCR circuit with L = 138 H, C = 34 muF, R = 89 ohm?\n",
        "input": "Q-value = (1 / R) * sqrt(L / (C * 0.000001))",
        "output": "22.6\n"
    },
    {
        "instruction": "What is the side of a cube of volume 167.472 cm3 (in m).\n",
        "input": "Volume = side^3",
        "output": "5512062\nCube of the side is it's volume."
    },
    {
        "instruction": "A body of mass 7 kg moving initially with a constant speed of 2 m/s to the north is subject to a constant force of 98 N directed towards the south for 30 s. Take the instant the force is applied to be t = 0, the position of the body at that time to be x = 0, and predict its position at t = 10 s.",
        "input": "m = 7 kg\nv = 2 m/s\nF = 98 N\nt = 10 s\ns = v * t - (F * (t^2)) / (2 * m)",
        "output": "-680\nThe position at time t = 10 s can be calculated using the formula: s = v * t - (F * (t^2)) / (2 * m)."
    },
    {
        "instruction": "A rigid bar of mass 2 kg is supported symmetrically by three wires each 18 m long. Those at each end are of material-1 and the middle one is of material-2. Find ratios of their diameters all have the same tension (Young's modulus of material-1 is 124 x 10^9 Nm-2, material-2 is 13 x 10^9 Nm-2).",
        "input": "diameter_ratio = sqrt(Y2 / Y1)",
        "output": "The ratio of their diameters is 0.32."
    },
    {
        "instruction": "A raindrop of radius 384 mm falls from a height of 561 m above the ground. It falls with decreasing acceleration until at half its original height, it attains its maximum (terminal) speed, and moves with uniform speed thereafter. What is the work done by the gravitational force on the drop in the first and second half of its journey?",
        "input": "",
        "output": "The work done by the gravitational force on the raindrop can be calculated by using the formula W = (m * g * h) / 2, where m is the mass of the raindrop, g is the acceleration due to gravity, and h is the height. In the first and second half of its journey, the raindrop experiences gravitational force, and the work done by the gravitational force is equal to 651990.4 joules joules., this is the final answer 651990.4 joules"
    },
    {
        "instruction": "A small bulb is placed at the bottom of a tank containing liquid to a depth of 178 cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of the liquid is 1.84.",
        "input": "Formula: Area = \u03c0 * h\u00b2 * (k / (1 - k)), where h is the depth of the liquid in centimeters, and k is the reciprocal of the refractive index of the liquid.",
        "output": "This is the answer 4.17 m\u00b2, formula used is : Formula: Area = \u03c0 * h\u00b2 * (k / (1 - k)), where h is the depth of the liquid in centimeters, and k is the reciprocal of the refractive index of the liquid."
    },
    {
        "instruction": "A solid cylinder of mass 962 kg rotates about its axis with angular speed 4 rad/s. The radius of the cylinder is 19 m. What is the magnitude of angular momentum of the cylinder about its axis?",
        "input": "Angular Momentum = c * m * r\u00b2 * w",
        "output": "To calculate the magnitude of the angular momentum, we use the following formula:\n\nAngular Momentum = c * m * r\u00b2 * w\n\nWhere,\n- c = Constant for the object\n- m = Mass of the object\n- r = Radius or length of the object\n- w = Angular speed of the object\n\nThe value of the constant (c) depends on the type of object being considered:\n- For a solid cylinder: c = 1/2\n- For a solid sphere: c = 2/5\n- For a hollow sphere: c = 2/3\n- For a rod: c = 1/3\n\nSubstituting the given values into the formula, we find that the magnitude of the angular momentum is approximately 694564.0 kg\u00b7m\u00b2."
    },
    {
        "instruction": "Suppose that the electric field part of an electromagnetic wave in vacuum is E = 1806cos[1701y + 176367t]. What is the amplitude of the magnetic field part of the wave?",
        "input": "E0 = 1806 N/C",
        "output": "6.02e-06 tesla\n\nThe magnetic field amplitude can be calculated by dividing the electric field amplitude by the speed of light."
    },
    {
        "instruction": "Monochromatic light of wavelength of 3305 nm is incident on aa surface of refractive index 330.5. What is the wavelength, speed and frequenct of refracted light.\n",
        "input": "speed of light in water = c/refractive index, wavelength = speed of light in water/frequency",
        "output": "1.00e+01 nm , 9.08e+05 m/s and 9.08e+13 hz \nFrequency of light does not depend on the property of the medium in which it is travelling. Hence, the frequency of the refracted ray in water will be equal to the frequency of the incident or reflected light in air."
    },
    {
        "instruction": "If a diatomic gas of 1 moles at 89 atm and volume 39 lit is adiabatically changed to volume 10 lit, then what will be the pressure.\n",
        "input": "P1*(V1^1.4)=P2*(V2^1.4)",
        "output": "598.2atm\nTo calculate the final pressure of the diatomic gas after an adiabatic expansion, we can use the adiabatic equation: P1 * V1^\u03b3 = P2 * V2^\u03b3, where P1 and V1 are the initial pressure and volume, P2 and V2 are the final pressure and volume, and \u03b3 is the heat capacity ratio. The heat capacity ratio (\u03b3) for a diatomic gas is typically 7/5."
    },
    {
        "instruction": "What are the components of a vector (-71) i + (-80) j along the direction of (-8) i + (4) j?",
        "input": "component = (-71 * -8 + -80 * 4) / sqrt(-8^2 + 4^2)",
        "output": "The component is 27.7 units."
    },
    {
        "instruction": "A convex mirror produces a real image of height 15 cm at a distance of 65 cm from it of a real object having a height of 96 cm. At what distance is the object placed from the mirror?",
        "input": "Formula: m = v / u = hi / ho",
        "output": "To find the distance of the object from the mirror, we use the formula m = v / u = hi / ho, where m is the magnification, v is the distance of the image from the mirror, u is the distance of the object from the mirror, hi is the height of the image, and ho is the height of the object. By rearranging the formula, we can calculate u as u = (ho * v) / hi. By substituting the given values into the formula, we find that the object is placed at a distance of 416.0 cm from the mirror., this is the final The object is placed at a distance of 416.0 cm from the mirror."
    },
    {
        "instruction": "A bike starting with an initial velocity of 80 m/s travels on a straight road at a constant rate of 6 m/s\u00b2. What is the time taken to travel a distance of 403 m?",
        "input": "initial velocity (u) = 80 m/s, acceleration (a) = 6 m/s\u00b2, distance (s) = 403 m",
        "output": "distance (s) = initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)\u00b2\n403 = 80 * t + 0.5 * 6 * t\u00b2\n403 = 344.0 + 55.46999999999999\n403 = 403\n\n0.5 * 6 * t\u00b2 + 80 * t - 403 = 0\n3.0 * t\u00b2 + 80 * t - 403 = 0\n\nUsing quadratic formula, we get:\n\nt = (-80 \u00b1 \u221a(80\u00b2 - 4 * 3.0 * (-403))) / (2 * 3.0)\nt = (-80 \u00b1 \u221a(6400 - 4836)) / 6\nt = (-80 \u00b1 \u221a(11236)) / 6\nt = (-80 \u00b1 \u221a(11236)) / 6\nt = (-80 \u00b1 \u221a(11236)) / 6\nt = (-80 \u00b1 106.0) / 6\nt = 4.333333333333333 or -31.0\nt = 4.3 or 4.3\n\nSince time cannot be negative, t = 4.3"
    },
    {
        "instruction": "A square coil of side 25 cm consists of 32 turns and carries a current of 7 A. The coil is suspended vertically, and the normal to the plane of the coil makes an angle of 59 degrees with the direction of a uniform horizontal magnetic field of magnitude 10 tesla. What is the magnitude of the torque experienced by the coil.",
        "input": "Torque = n * b * i * A * sin(d)",
        "output": "To calculate the magnitude of the torque experienced by the coil, we use the following formula:\n\nTorque = n * b * i * A * sin(d)\n\nWhere,\n- n = Number of turns in the coil\n- b = Magnetic field\n- i = Current in the coil\n- A = Area of the coil\n- d = Angle between the normal to the coil and the magnetic field\n\nFor a square coil, the area (A) is equal to the square of the side length (l) of the coil. For a circular coil, the area (A) is equal to pi times the square of the radius (l) of the coil.\n\nSubstituting the given values into the formula and evaluating it, we find that the magnitude of the torque experienced by the coil is approximately 120.0 newton-m."
    },
    {
        "instruction": "A solid sphere rolls down two different inclined planes of heights 20 and 13 and with angles of inclination of 69 and 44, on which it will reach the ground faster?",
        "input": "time = sqrt(height * (k + 1)) / sin(angle)",
        "output": "To compare the times, we use the following formula:\n\ntime = sqrt(height * (k + 1)) / sin(angle)\n\nSubstituting the given values into the formula, we find that:\n\nThe first plane takes less time to reach the ground."
    },
    {
        "instruction": "A bat emits ultrasonic sound of frequency 140700 Hz in air. If this sound meets a water surface, what is the wavelength of the reflected sound? (Speed of sound in air = 340 ms-1 and in water = 1486 ms-1)\n",
        "input": "wavelength of refracted sound = speed of sound in air/frequency of the ultrasonic sound",
        "output": "2.42e-03 m\nGiven that the speed of sound in air is 340 m/s and the speed of sound in water is 1486 m/s, we can substitute these values into the formula to calculate the wavelength. For the sound emitted in air: \u03bb_air = (340 m/s) / 140700 Hz, For the sound reflected in water: \u03bb_water = (1486 m/s) / 140700 Hz"
    },
    {
        "instruction": "Two masses each of mass 98 kg are attached by a spring with K = 106 Nm-1. If a force of 134 N is applied at the free ends of both masses, then what is the time period of oscillation?",
        "input": "Formula: T = 2\u03c0\u221a(m / (2k)), where T is the time period of oscillation, m is the mass of each mass (98 kg), and k is the spring constant (106 Nm-1).",
        "output": "Using this formula: Formula: T = 2\u03c0\u221a(m / (2k)), where T is the time period of oscillation, m is the mass of each mass (98 kg), and k is the spring constant (106 Nm-1)., this is the final answer derived: 4.27e+00 s"
    },
    {
        "instruction": "A series LCR circuit is connected to a variable frequency 230 V source with L = 163 H, C = 111 muF, R = 78 ohm. Determine the RMS potential drop across inductance?",
        "input": "RMS Potential Drop across Inductance = Current RMS * \u03c9_r * L",
        "output": "3.57e+03 volt"
    },
    {
        "instruction": "What is the gravitational field at a point P at a distance of 268 m from a mass of 341 kg?",
        "input": "Gravitational Field (g) = cal3(341, 268) N/kg",
        "output": "The gravitational field at a point P at a distance of 268 m from a mass of 341 kg is given by the formula g = (-G * m) / (r^2), where G is the gravitational constant, m is the mass, and r is the distance. Plugging in the values, we get g = -3.17e-13 N/kg."
    },
    {
        "instruction": "A concave lens produces a real image at a distance of 63 cm from it of a real object having a height of 79 cm and placed 158 cm in front of it. What is the height of the image?",
        "input": "Formula: hi = (v * ho) / u",
        "output": "To find the height of the image, we use the formula hi = (v * ho) / u, where hi is the height of the image, ho is the height of the object, u is the distance of the object from the lens, and v is the distance of the image from the lens. By substituting the given values into the formula, we can solve for hi. In this case, the height of the image is 31.5 cm., this is the final The height of the image is 31.5 cm."
    },
    {
        "instruction": "A rope of negligible mass is wound round a solid sphere of mass 23 kg and radius 4 cm. What is the angular acceleration of the solid sphere if the rope is pulled with a force of 8 N? Assume that there is no slipping.",
        "input": "Acceleration = Force / (k * mass * radius)",
        "output": "Acceleration = 8 N / (0.4 * 23 kg * 4 cm)\n\nTo calculate the angular acceleration of the solid sphere, we use the following formula:\n\nAcceleration = Force / (k * mass * radius)\n\nSubstituting the values:\n\nForce = 8 N\nk = 0.4\nMass = 23 kg\nRadius = 4 cm\n\nWe find that the angular acceleration of the solid sphere is approximately 21.7 rad/s\u00b2."
    },
    {
        "instruction": "A body is dropped from a height of 5396 m with an initial velocity of 79 m/s. With what velocity will it strike the ground?",
        "input": "height (h) = 5396 m, initial velocity (u) = 79 m/s",
        "output": "final velocity (v) = \u221a(initial velocity (u)\u00b2 + 2 * acceleration (g) * height (h))\nv = \u221a(79\u00b2 + 2 * 9.8 * 5396)\nv = \u221a(6241 + 105761.6)\nv = \u221a112002.6\nv = \u221a334.7\nv = 334.7"
    },
    {
        "instruction": "A toroid has a core of inner radius 123 cm and outer radius 167 cm, around which 177 turns of a wire are wound. If the current in the wire is 4 A, what is the magnetic field inside the core of the solenoid.",
        "input": "Magnetic field = (mu * n * i) / l",
        "output": "To calculate the magnetic field inside the toroid, we use the following formula:\n\nMagnetic field = (mu * n * i) / l\n\nWhere,\n- n = Number of turns of the wire\n- i = Current in the wire\n- l = Length of the wire\n\nWe calculate the length of the wire using the formula:\n- Length of the wire = (r1 + r2) * pi\n\nSubstituting the given values and evaluating the formula, we find that the magnetic field inside the core of the toroid is approximately 9.77e-05 tesla."
    },
    {
        "instruction": "A train runs along an unbanked circular track of radius 426 m at a speed of 44 m/s. The mass of the train is 73 kg. What is the angle of banking required to prevent wearing out of the rail?",
        "input": "((atan((v^2) / ((param + 400) * g))) * 180) / pi",
        "output": "24\nTo calculate the angle of banking, we use the formula ((atan((v^2) / ((param + 400) * g))) * 180) / pi, where v is the speed (44 m/s), g is the acceleration due to gravity (10 m/s^2), and param is the radius (426 m) of the circular track."
    },
    {
        "instruction": "A closely wounded solenoid of 360 turns and an area of cross-section 0.0078 m\u00b2 carries a current of 8 A. What is its associated magnetic moment?",
        "input": "n * i * A",
        "output": "The magnetic moment (m) of a solenoid is given by the formula m = n * i * A, where 'n' is the number of turns, 'i' is the current, and 'A' is the area of cross-section. Substituting the given values, we have m = 360 * 8 * 0.0078 = 22.464."
    },
    {
        "instruction": "What is the mass of an object with kinetic energy of 499209 J moving with a velocity of 438 m/s?",
        "input": "m = (2 * KE) / v^2",
        "output": "To calculate the mass, we use the formula m = (2 * KE) / v^2, where m is the mass, KE is the kinetic energy (499209 J), and v is the velocity (438 m/s)., this is the final answer 5.2"
    },
    {
        "instruction": "Two absolute scales A and B have triple points of water defined to be 221 A and 416 B. What is the relation between TA and TB?",
        "input": "Relation between TA and TB = TA / TB",
        "output": "To find the relation between TA and TB, we divide the temperature on scale A (TA) by the temperature on scale B (TB). Therefore, the relation is given by:\n\nRelation between TA and TB = TA / TB\n\nSubstituting the given values, we find that the relation is approximately 0.53."
    },
    {
        "instruction": "To maintain a rotor at a uniform angular speed of 671 rad/s, an engine needs to transmit a torque of 833 Nm. What is the power required by the engine?",
        "input": "Power = Angular Speed * Torque",
        "output": "Power = 671 rad/s * 833 Nm\n\nTo calculate the power required by the engine, we use the following formula:\n\nPower = Angular Speed * Torque\n\nSubstituting the values:\n\nAngular Speed = 671 rad/s\nTorque = 833 Nm\n\nWe find that the power required by the engine is 558943 watts."
    },
    {
        "instruction": "Calculate the energy of each of the photons which correspond to light of frequency 247153 Hz.\n",
        "input": "Energy = h*frequency",
        "output": "1.63e-28joules\nTo calculate the energy of a photon, you can use the formula: E = h * f, where E is the energy of the photon, h is the Planck constant (approximately 6.626 x 10^-34 J\u00b7s), and f is the frequency of the light."
    },
    {
        "instruction": "What is the gravitational potential at a point P at a distance of 308 m from the center of the uniform solid sphere of radius 361 m and mass 73 kg?",
        "input": "Gravitational Potential (V) = cal1(73, 308, 361) joule/kg",
        "output": "The gravitational potential at a point P at a distance of 308 m from the center of the uniform solid sphere of radius 361 m and mass 73 kg is given by the formula V = (-G * m * (3 * R^2 - r^2)) / (2 * R^3), where G is the gravitational constant, m is the mass, r is the distance, and R is the radius. Plugging in the values, we get V = -1.53e-11 joule/kg."
    },
    {
        "instruction": "An object of mass 552 g stands on a weighing machine in a lift, which is moving downwards with a uniform speed of 826 cm/s.",
        "input": "Scale Reading = m * 10 - v",
        "output": "4694\nTo calculate the scale reading, we use the formula Scale Reading = mass * 10 - velocity, where the mass is 552 g and the velocity is 826 cm/s."
    },
    {
        "instruction": "What is the lowest total resistance that can be secured by combinations of three coils of resistance 140, 89, 52?",
        "input": "R_total = (R1 * R2 * R3) / (R1 * R2 + R2 * R3 + R3 * R1)",
        "output": "The lowest combination of resistances can be obtained by connecting them in parallel. The total resistance is calculated as (140 * 89 * 52) / (140 * 89 + 89 * 52 + 52 * 140) = 26.6 ohm.\n\nTo calculate the lowest combination of resistances, we connect them in parallel. The total resistance (R_total) is given by the formula (R1 * R2 * R3) / (R1 * R2 + R2 * R3 + R3 * R1), where R1, R2, and R3 are the individual resistances."
    },
    {
        "instruction": "A body is dropped from the top of a building with an initial velocity of 696 m/s under gravity, and it reaches the ground after 192 s. What is the height of the building?",
        "input": "initial velocity (u) = 696 m/s, time (t) = 192 s",
        "output": "height (s) = initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)\u00b2\ns = 696 * 192 + 0.5 * 9.8 * 192\u00b2\ns = 133632 + 180633.6\ns = 314265.6"
    },
    {
        "instruction": "An electric appliance of 32247 W power rating is operated in a domestic electric circuit of 233 V that has a current rating of 93.1 A. Will the appliance be safe for a longer time?",
        "input": "P/V - I",
        "output": "It will be safer if P/V - I is less than or equal to 0.01. Now P/V - I = 32247/233 - 93.1 = 45.299. So, it will not be safe for a longer time."
    },
    {
        "instruction": "A person with a myopic eye cannot see objects beyond 84410 mm distinctly. What should be the type of the corrective lens used to restore proper vision?\n",
        "input": "1/f=1/v-1/u",
        "output": "the remedial lens should make the objects at infinity appear at far point, hence u = infinity, v = far point of defected eye, from P=1/f, 1/f=1/v-1/u, we get P=1/v-1/u, P=1/v-0=1/v, implies P = 0.01 diatrope, type of lens required is concave.\n"
    },
    {
        "instruction": "A body is dropped from a height of 6559 m with an initial velocity of 88 m/s. With what velocity will it strike the ground?",
        "input": "height (h) = 6559 m, initial velocity (u) = 88 m/s",
        "output": "final velocity (v) = \u221a(initial velocity (u)\u00b2 + 2 * acceleration (g) * height (h))\nv = \u221a(88\u00b2 + 2 * 9.8 * 6559)\nv = \u221a(7744 + 128556.40000000001)\nv = \u221a136300.40000000002\nv = \u221a369.2\nv = 369.2"
    },
    {
        "instruction": "An LC circuit contains a 174 mH inductor and a 147 muF capacitor with an initial charge of 39 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0. At what time(s) energy stored in magnetic form is 7 percent of total energy?",
        "input": "Time = n * T, where n is an integer\nT = 1 / (Natural Frequency)",
        "output": "0.04t, 0.54t, 1.04t, ...; where t = 3.18e-02 s"
    },
    {
        "instruction": "A convex lens produces 74 times magnified real image of an object placed at 85.89 cm in front of it. At what distance is the image formed from the lens?",
        "input": "Formula: v = n * u",
        "output": "To find the distance at which the image is formed from the lens, we use the formula v = n * u, where v is the distance of the image from the lens, n is the magnification factor, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for v. In this case, the image is formed at a distance of 6355.9 cm from the lens., this is the final The image is formed at a distance of 6355.9 cm from the lens."
    },
    {
        "instruction": "Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapor, and other constituents) in a room of capacity 39 m3 at a temperature of 92 degree C and 1 atm pressure.",
        "input": "total_number_of_molecules = (p * v) / (k * t1)",
        "output": "7.742703990470519e+26 molecules\nHere, p = 1 atm = 100000 Pa, v = 39 m3, t1 = 92 degree C = 365 K, k = 1.38 x 10^-23 J/K"
    },
    {
        "instruction": "A 30 pF capacitor is charged by a 164 V supply. It is then disconnected from the supply and is connected to another uncharged 132 pF capacitor. How much electrostatic energy is lost in this process?",
        "input": "Formula: (403440.0 - 328728.8888888889) * 10^(-12)\nValues: c1 = 30 pF, c2 = 132 pF, v = 164 V",
        "output": "Answer:7.47e-08 joule\n\nExplanation: The electrostatic energy lost in the process can be calculated by subtracting the final energy from the initial energy:\n\nE_loss = E_initial - E_final\n\nThe initial energy E_initial can be calculated as 0.5 * C1 * V^2, where C1 is the capacitance of the first capacitor and V is the voltage. The final energy E_final can be calculated as 0.5 * C3 * V^2, where C3 is the equivalent capacitance when the two capacitors are combined.\n\nSubstituting the given values, we have:\n\nE_loss = 403440.0 joule - 328728.8888888889 joule = E_loss = 7.47e-08 joule joule."
    },
    {
        "instruction": "An image is formed by a convex lens of focal length 35 cm at a distance of 157 cm behind it. Find at what distance object is placed in front of lens.",
        "input": "Formula: 1/f = 1/v - 1/u for convex lens.",
        "output": "To find the distance of the object from the lens, we use the formula for convex lenses: 1/f = 1/v - 1/u, where f is the focal length ofthe lens, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 45.0 cm from the lens., this is the final The object is placed at 45.0 cm in front of the lens."
    },
    {
        "instruction": "Find the focal length of a concave mirror whose radius of curvature is 5008.36 cm.",
        "input": "Formula: f = R/2",
        "output": "To find the focal length of a concave mirror, we use the formula f = R/2, where f is the focal length and R is the radius of curvature. By substituting the given value of R into the formula, we can solve for f. In this case, the focal length is 2504.2 cm., this is the final 2504.2"
    },
    {
        "instruction": "A solid cylinder of radius 413 m weighs 65 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 24 m/s. How much work has to be done to stop it?\n",
        "input": "0.5*(0.5+1)*m*v*v",
        "output": "37440.0 joules\n"
    },
    {
        "instruction": "Given observations (tuples of I (in A) and V (in V)): (36, 612), (11, 187), (14, 238), (15, 255), (18, 306), (22, 374); Determine whether the given conductor is an ohmic conductor or not.\n",
        "input": "",
        "output": "Yes, it is an ohmic conductor.\n"
    },
    {
        "instruction": "A vertical off-shore structure is built to withstand a maximum stress of 7840000 Pa. Is the structure suitable for putting up on top of an oil well in the ocean? Take the depth of the ocean to be roughly 8 km, and ignore ocean currents?",
        "input": "8 * 1000 * 980",
        "output": "no, it is not suitable"
    },
    {
        "instruction": "A parallel plate capacitor made of circular plates of radius r = 123 cm has a capacitance C = 55 pF. The capacitor is connected to a 230 V ac supply with an angular frequency of 1350 rad/s. What is the rms value of the conduction current?",
        "input": "I = 1.71e-05 ampere",
        "output": "1.71e-05 ampere\n\nThe rms value of the conduction current can be calculated by taking the square root of the average of the square of the current."
    },
    {
        "instruction": "A black box has a net outward flux of 1854972 N\u00b7m\u00b2/C through its surface. What is the net charge inside the box?\n",
        "input": "Net charge = Flux * epsilon_0",
        "output": "To determine the net charge inside the box, we use the formula:\nNet charge = Flux * epsilon_0\nGiven flux = 1854972 N\u00b7m\u00b2/C,\nNet charge = 1.64e-05 C\n"
    },
    {
        "instruction": "A sound wave travels at a speed of 158725.2 m/s, if it's wavelength is 4 m, will the sound wave be audible ? \n",
        "input": "frequency = wave speed / wavelength",
        "output": "not audible\nWhether a sound wave is audible or not depends on its frequency, not its wavelength. Audible sound waves have frequencies within the range of human hearing, which is typically between 20 Hz and 20,000 Hz. To determine if a sound wave is audible, we need to calculate its frequency using the wave speed and wavelength. The formula to calculate the frequency of a sound wave is: f = v / \u03bb, where f is the frequency, v is the wave speed, and \u03bb is the wavelength. Substituting the given values into the formula, we can calculate the frequency of the sound wave: f = 158725.2 m/s / 4 m. Now, we can compare the calculated frequency to the audible frequency range (20 Hz to 20,000 Hz) to determine if the sound wave is audible or not."
    },
    {
        "instruction": "A steam engine delivers 752 J of work per minute and services 807 J of heat per minute from its boiler. How much heat is wasted per minute?\n",
        "input": "Efficiency = Work per minute/Heat per minute from its boiler, Heat Wasted = Heat per minute - (Efficiency/100)*Heat per minute",
        "output": "55 joules\nThe efficiency of an engine can be calculated using the formula: Efficiency = (Work output / Heat input) * 100"
    },
    {
        "instruction": "A 9721 N force is applied on a body placed on a smooth surface resulting in acceleration of 808 m/s^2, then what is the mass of the body?",
        "input": "m = F / a",
        "output": "12.0\nTo calculate the mass, we use the formula m = F / a, where m is the mass, F is the force (9721 N), and a is the acceleration (808 m/s^2)."
    },
    {
        "instruction": "A 153 microfarad capacitor is connected to a 174 V, 50 Hz ac supply. Determine the rms value of current in the circuit?",
        "input": "X_c_inverse = 2 * pi * f * C * 0.000001\nI_rms = V * X_c_inverse",
        "output": "8.36e+00 ampere"
    },
    {
        "instruction": "Two objects of masses 14 g and 8 g are moving along the same line and direction with velocities of 10 m/s and 23 m/s respectively. They collide and after the collision, the second object moves at a velocity of 22 m/s. Determine the velocity of the first object.",
        "input": "v1 = ((m1 * u1) + (m2 * u2) - (m2 * v2)) / m1",
        "output": "To find the velocity of the first object (v1), we use the formula:\n\nv1 = ((m1 * u1) + (m2 * u2) - (m2 * v2)) / m1\n\nSubstituting the given values, we have:\n\nv1 = ((14 * 10) + (8 * 23) - (8 * 22)) / 14\n\nSimplifying the expression gives us v1 = 10.6 m/s."
    },
    {
        "instruction": "What is the gravitational potential at a point P at a distance of 137 m from the center of the spherical shell of radius 148 m and having -1.19e+02 C charge distributed uniformly on it.\n",
        "input": "To calculate the gravitational potential at a point outside a uniformly charged spherical shell, we use the formula:\n\nV = (k * Q) / R\n\nwhere V is the gravitational potential, k is the electrostatic constant (9 * 10^9 Nm^2/C^2), Q is the charge, and R is the distance from the center of the shell.",
        "output": "-7.24e+09 joule/coulomb\n"
    },
    {
        "instruction": "A hole is drilled in a copper sheet. The diameter of the hole is 54 cm at 79 degree C. What is the change in the diameter of the hole when the sheet is heated to 452 degree C? Coefficient of linear expansion of copper = 1.7 x 10-5K-1.",
        "input": "Change in diameter = initial diameter * sqrt(1 + (coefficient of linear expansion * initial diameter * (final temperature - initial temperature))) - initial diameter",
        "output": "To calculate the change in diameter, we use the following formula:\n\nChange in diameter = initial diameter * sqrt(1 + (coefficient of linear expansion * initial diameter * (final temperature - initial temperature))) - initial diameter\n\nSubstituting the given values into the formula, we find that the change in diameter is approximately 8.566 cm."
    },
    {
        "instruction": "An LC circuit contains a 115 mH inductor and a 51 muF capacitor with an initial charge of 29 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0. What is the initial energy stored, is it conserved during LC oscillations?",
        "input": "Initial Energy = 0.5 * (Charge^2) * (1 / Capacitance)",
        "output": "8.25e+00 joule, it is conserved during oscillations."
    },
    {
        "instruction": "Light enters from a material-1 to material-2 having refractive index 7.0. If the speed of light in material-1 and material-2 is 91000000 m/s and 210000000 m/s respectively, what is the refractive index of material-1?",
        "input": "Refractive Index (n) = (n2 * v2) / v1",
        "output": "The refractive index of a material can be calculated using the formula n = (n2 * v2) / v1, where n is the refractive index of material-1, n2 is the refractive index of material-2, v1 is the speed of light in material-1, and v2 is the speed of light in material-2., this is the final 16.2"
    },
    {
        "instruction": "A convex lens produces 37 times diminished real image of a 72.57 cm object placed in front of it. What is the height of the image formed by the lens?",
        "input": "Formula: hi = ho / n",
        "output": "To find the height of the image formed by the lens, we use the formula hi = ho / n, where hi is the height of the image, ho is the height of the object, and n is the magnification factor. By substituting the given values into the formula, we can solve for hi. In this case, the height of the image formed by the lens is 2.0 cm., this is the final The height of the image formed by the lens is 2.0 cm."
    },
    {
        "instruction": "If a gas molecule has average velocity of 1460 m/s and is at a temperature 1 degree C. What is the molar mass of the gas.",
        "input": "(3 * r * t1 * 1000) / (math.pi * v * v)",
        "output": "1.567287933823682 m/s\n The formula used is: (3 * r * t1 * 1000) / (math.pi * v * v)"
    },
    {
        "instruction": "A circular coil of wire consisting of 54 turns, each of radius 484 cm placed in a horizontal plane carries a current of 19 A in anticlockwise direction. What is the magnitude and direction of the magnetic field B at the center of the coil?",
        "input": "B = (mu * n * i) / (2 * r)",
        "output": "To calculate the magnetic field B at the center of the coil, we use the following formula:\n\nB = (mu * n * i) / (2 * r)\n\nWhere,\n- B = Magnetic field at the center of the coil\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- n = Number of turns in the coil\n- i = Current flowing through the coil\n- r = Radius of the coil\n\nSubstituting the given values into the formula, we find that the magnitude of the magnetic field B is approximately 1.33e-04 tesla vertically upwards."
    },
    {
        "instruction": "In a process, 7352 J of heat is absorbed by a system and 8272 J of work is done by the system. What is the change in internal energy for the process ?\n",
        "input": "\u0394U = Q+W",
        "output": "from first law of thermodynamics, du = q + w => du = (+7352) + (-8272) => du = -920joule\nQ is positive and W is negative as heat is absorbed by a system and work is done by system."
    },
    {
        "instruction": "If a car has an initial velocity of 59 m/s and has a constant acceleration of 33 m/s\u00b2 for 29 s, then what is the final velocity of the car?",
        "input": "final_velocity = initial_velocity + (acceleration * time)",
        "output": "The final velocity of the car is 1016 m/s."
    },
    {
        "instruction": "What is the velocity of an object of mass 260 kg having kinetic energy of 499979 J?",
        "input": "v = sqrt((2 * KE) / m)",
        "output": "To calculate the velocity, we use the formula v = sqrt((2 * KE) / m), where v is the velocity, KE is the kinetic energy (499979 J), and m is the mass (260 kg)., this is the final answer 62.0"
    },
    {
        "instruction": "A wheel starting with an initial angular velocity of 77 rad/s accelerates with a constant angular acceleration of 75 rad/s\u00b2. If it reaches an angular position of 54 rad, then what is its final velocity?",
        "input": "final_angular_velocity = sqrt(initial_angular_velocity^2 + (2 * angular_acceleration * angular_position))",
        "output": "To calculate the final angular velocity, we use the following formula:\n\nfinal_angular_velocity = sqrt(initial_angular_velocity^2 + (2 * angular_acceleration * angular_position))\n\nSubstituting the given values into the formula, we find that the final angular velocity is approximately 118.4 rad/s."
    },
    {
        "instruction": "In a Youngs double-slit experiment, the slits are seperated by 0.07 mm and the screen is placed 2.0 m away. The distance between the central bright fringe and the 7 bright fringe is measured to be 4 cm. Determine the wavelength of the ligth used for the experiment.\n",
        "input": "Distance between central bright fringe and bright fringe = (wavelength of light*distance from screen)/distance between slits",
        "output": "2.00e-07 m\nIn a Young's double-slit experiment, the wavelength of light can be determined using the formula: \u03bb = (d * sin(\u03b8)) / n, where \u03bb is the wavelength of light, d is the separation between the slits, \u03b8 is the angle of the fringe (in radians), and n is the order of the fringe."
    },
    {
        "instruction": "A body is dropped from a height of 8288 m with an initial velocity of 60 m/s. With what velocity will it strike the ground?",
        "input": "height (h) = 8288 m, initial velocity (u) = 60 m/s",
        "output": "final velocity (v) = \u221a(initial velocity (u)\u00b2 + 2 * acceleration (g) * height (h))\nv = \u221a(60\u00b2 + 2 * 9.8 * 8288)\nv = \u221a(3600 + 162444.80000000002)\nv = \u221a166044.80000000002\nv = \u221a407.5\nv = 407.5"
    },
    {
        "instruction": "An object is placed at 409 cm in front of a convex lens. Image is formed at a distance of 358 cm behind it. Find the focal length of the lens.",
        "input": "Formula: 1/f = 1/v - 1/u for convex lens.",
        "output": "To find the focal length of the lens, we use the formula for convex lenses: 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for f. In this case, the focal length of the lens is 190.9 cm., this is the final The focal length of the lens is 190.9 cm."
    },
    {
        "instruction": "An object is placed at 543 cm in front of a convex lens. Image is formed at a distance of 1329 cm in front of it. Find the focal length of the lens.",
        "input": "Formula: 1/f = 1/v - 1/u for convex lens.",
        "output": "To find the focal length of the lens, we use the formula for convex lenses: 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for f. In this case, the focal length of the lens is 918.1 cm., this is the final The focal length of the lens is 918.1 cm."
    },
    {
        "instruction": "The coefficient of linear expansion of steel is 3.6e-05 K^-1. What is the change in its volume 63 m^3 for a rise in temperature from 20 degree C to 393 degree C?",
        "input": "Change in volume = d1 * a * (t2 - t1)",
        "output": "To find the change in volume, we use the following formula:\n\nChange in volume = d1 * a * (t2 - t1)\n\nSubstituting the given values into the formula, we find that the change in volume is approximately 0.85 m^3."
    },
    {
        "instruction": "If 956 coulomb of charge flows through any section of a conductor in 173 s, what is the value of current?",
        "input": "I = Q / t",
        "output": "5.5 ampere\n\nThe value of the current can be calculated using the formula: I = Q / t, where Q is the charge and t is the time."
    },
    {
        "instruction": "What is the pressure inside a drop of liquid of radius 2 mm at room temperature? Surface tension of liquid at that temperature (274 K) is 400 x 10^(-3) Nm^(-1). Also give the excess pressure inside the drop.",
        "input": "excess pressure = (2 * surface tension) / radius, total pressure = 1.01 * (10 ** 5) + excess pressure",
        "output": "The excess pressure inside the drop is 400.00 pascal. The total pressure inside the drop is 1.01e+05 pascal."
    },
    {
        "instruction": "If a diatomic gas of 10 moles at 167 atm and volume 167 lit is isothermally changed to volume 32 lit, then what will be the pressure.\n",
        "input": "P1*V1 = P2*V2",
        "output": "871.5atm\nTo determine the final pressure of a diatomic gas after an isothermal expansion, we can use Boyle's Law, which states that for an ideal gas at constant temperature: P1 * V1 = P2 * V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume."
    },
    {
        "instruction": "What is the gravitational force between two masses 17000 kg and 98000 kg seperated bt a distance 73 m. G = 6.67 x 10-11\n",
        "input": "f = (g x m1 x m2)/d^2",
        "output": "the gravitational between two bodies of masses m1 and m2 seperated by a distance d is given by, f = (g x m1 x m2)/d^2 = (6.67 x 10^-11 x 17000 x 10^-3 x 98000 x 10^-3)/73^2 = 2.09e-05 newton\n"
    },
    {
        "instruction": "A capacitor made of two circular plates of radius 80 cm, and separated by 177 cm. The capacitor is being charged by an external source. The charging current is constant and equal to 192 mA. Calculate the rate of charge of potential difference between the plates?",
        "input": "I = 192 mA, C = 1.01e-11 farad",
        "output": "1.91e+10 volt/s\n\nThe rate of change of potential difference between the plates can be calculated using the formula: dV/dt = I / C, where I is the charging current and C is the capacitance."
    },
    {
        "instruction": "A end of string of mu = 0.008 kgm-1 is connected to tuning fork of nu = 185 Hz. The other end passes over a pulley and is tied to a mass of 50 kg. The pulley end is such that reflected waves at this end have negligible amplitude. At t = 0, the fork end of the string x = 0 has y = 0 and is moving along +ve y axis. The amplitude of the wave is 8 cm. Write down y as function of x,t that describes the wave on the string.\n",
        "input": "wavelength = speed/frequency",
        "output": "0.08 sin(1.6e+03t - 4.7e+00x)\nto form wave equation, we have to find amplitude, frequency, velocity of wave. given, amplitude = 8 cm = 0.08 m ,frequency = 185 hz ,v = sqrt(t/mu) = sqrt(490.0/0.008) = 247.5 ,w = 2*pi*v = 2*3.14*247.5 = 1555.0 ,wavelength = v/freq = 247.5/185 ,k = 2*pi/wavelength =  2*pi*185/247.5 = 4.7 ,the equation of the wave is, v(x,t) = a sin(wt-kx), "
    },
    {
        "instruction": "A force of 100 +/- 10 N is applied over an area of 3.41 +/- 0.01 m2. Calculate the pressure exerted over the area.\n",
        "input": "Pressure = Force/Area",
        "output": "29.33+/-3.02\nTo calculate the pressure exerted over an area, we use the formula: Pressure = Force / Area. In this case, the force applied is 100 N, and the area is 3.41 m\u00b2. The error in the force measurement is 10 N, and the error in the area measurement is 0.01 m\u00b2. To determine the error in the pressure calculation, we can use error propagation. The formula for calculating the maximum error in a function involving measured quantities is: Max Error = |dP/dx| * \u0394x, where Max Error is the maximum error, dP/dx is the derivative of the function with respect to the measured quantity (force or area), and \u0394x is the error in the measured quantity. Taking the derivative of the pressure formula with respect to force and area, we have: dP/dF = 1 / A, dP/dA = -F / A\u00b2. Substituting the given values into the error propagation formula, we can calculate the maximum error in the pressure: Max Error = |(1 / A_val) * F_error| + |(-F_val / A_val\u00b2) * A_error|. Now, we can substitute the given values to calculate the pressure and its maximum error over the given area."
    },
    {
        "instruction": "Two heavy spheres each of mass 145 kg, 73 kg respectively are placed 47 m apart on a horizontal table. What is the gravitational potential at the mid point of the line joining the centres of the spheres?",
        "input": "Gravitational Potential (V) = -6.19e-10 joule/kg",
        "output": "The gravitational potential at the mid point of the line joining the centres of the spheres is given by the formula V = (-1 * G * m1 / R) - (G * m2 / R), where G is the gravitational constant, m1 and m2 are the masses of the spheres, and R is the distance between them. Plugging in the values, we get V = -6.19e-10 J/kg."
    },
    {
        "instruction": "An image is formed by a convex lens of focal length 285 cm at a distance of 773 cm in front of it. Find at what distance object is placed in front of lens.",
        "input": "Formula: 1/f = 1/v - 1/u for convex lens.",
        "output": "To find the distance of the object from the lens, we use the formula for convex lenses: 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 208.2 cm from the lens., this is the final The object is placed at 208.2 cm in front of the lens."
    },
    {
        "instruction": "A child stands at the centre of a turntable with his arms outstretched. The turntable is rotating with an angular speed of 140 rad/s. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to 44/141 times the initial value?",
        "input": "Angular Speed = (n2 * w) / n1\nKinetic Energy Ratio = (n2^3) / (n1^3)",
        "output": "To calculate the angular speed and kinetic energy ratio, we use the following formulas:\n\nAngular Speed = (n2 * w) / n1\nKinetic Energy Ratio = (n2^3) / (n1^3)\n\nWhere,\n- n1 = Initial moment of inertia\n- n2 = Reduced moment of inertia\n- w = Initial angular speed\n\nSubstituting the given values into the formulas, we find that the angular speed of the child is approximately 448.6 rad/s rad/s."
    },
    {
        "instruction": "A 44 ohm resistor is connected to a 226 V, 27 Hz ac supply. What is the rms value of current in the circuit?",
        "input": "I_rms = V / R",
        "output": "5.14e+00 ampere"
    },
    {
        "instruction": "A convex mirror produces a real image of height 723 cm of a real object of height 1172 cm placed in front of it. What is the magnification of the mirror?",
        "input": "Formula: m = hi / ho = v / u",
        "output": "To find the magnification of the convex mirror, we use the formula m = hi / ho = v / u, where m is the magnification, hi is the height of the image, ho is the height of the object, v is the distance of the image from the mirror, and u is the distance of the object from the mirror. Since the heights are provided instead of distances, the formula still holds. By substituting the given values into the formula, we can calculate the magnification. In this case, the magnification of the mirror is 0.6., this is the final The magnification of the mirror is 0.6."
    },
    {
        "instruction": "What is the largest average velocity of blood flow in an artery of radius 1492 micrometer and length 1719 mm if flow must remain laminar? What is the corresponding flow rate?",
        "input": "(2000 * 2.084) / (1.06 * 2 * 1492)",
        "output": "The largest average velocity of blood flow is 1.32 m/s. The corresponding flow rate is 9.22e-06 m^3/s."
    },
    {
        "instruction": "A 54 kg mass, fastened to the end of a steel wire of initial length 10 m, is whirled in a vertical circle with an angular velocity of 6 rev/s at the bottom of the circle. The cross-sectional area of the wire is 60 mm^2. Calculate the elongation of the wire when the mass is at the lowest point of its path.",
        "input": "elongation = (force * length) / (A * 10^(-6) * Y_steel)",
        "output": "To calculate the elongation, we use the formula:\n\nelongation = (force * length) / (A * 10^(-6) * Y_steel)\n = (54 kg * (9.8 + 10 m * \u03c0^2 * 6^2) * 10 m) / (60 mm^2 * 10^(-6) m^2 * (2 * 10^11 N/m^2))\n = 16.0 cm."
    },
    {
        "instruction": "An object is projected with an initial velocity of 714 m/s, if the horizontal range of the object is 2595 m, what is the angle of projection?",
        "input": "v = 714 m/s, h = 2595 m",
        "output": "1, 89"
    },
    {
        "instruction": "A body of mass 11 kg is hanged from the roof with the help of a steel wire of length 10 m. Another body of mass 16 kg is hanged from the bottom of mass m1 with the help of a steel wire of length 9 m. If the radius of both wires is 96 x 10^(-4) m, what is the elongation of the steel wire?",
        "input": "elongation = (F * l) / (A * E)",
        "output": "elongation = (F * l) / (A * E)\nThe elongation of the wire is 4.6e-05 m."
    },
    {
        "instruction": "In a chamber, a uniform magnetic field of 0.0035 T is maintained. An electron is shot into the field with a speed of 13000000 m/s, making an angle of 13 degrees with the field. Determine the frequency of the revolution of the electron.",
        "input": "Frequency of revolution = (b * e) / (2 * pi * m)",
        "output": "To calculate the frequency of revolution, we use the following formula:\n\nFrequency of revolution = (b * e) / (2 * pi * m)\n\nSubstituting the given values:\n- b = 0.0035 T\n- e = 1.6000000000000002e-19 C\n- m = 9.1e-31 kg\n\nAfter evaluating the formula, we find that the frequency of revolution is approximately 9.79e+07 sec^-1."
    },
    {
        "instruction": "A 98 ohm resistor is connected to a 40 V, 160 Hz ac supply. What is the net power consumed over a full cycle?",
        "input": "P_net = (V ** 2) / R",
        "output": "1.63e+01 watt"
    },
    {
        "instruction": "A rigid bar of mass 15 kg is supported symmetrically by three wires each 17 m long. Those at each end are of material-1 and the middle one is of material-2. Find ratios of their diameters all have the same tension (Young's modulus of material-1 is 168 x 10^9 Nm-2, material-2 is 88 x 10^9 Nm-2).",
        "input": "diameter_ratio = sqrt(Y2 / Y1)",
        "output": "The ratio of their diameters is 0.72."
    },
    {
        "instruction": "For the travelling harmonic wave y(x, t) = 21 cos 2\u03c0 (50t \u2013 0.025x + 0.35) where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of 4 m?\n",
        "input": "Phase difference = (2pi/wavelength)* Path difference",
        "output": "20.0 \u03c0 rad\nTo calculate the phase difference between two points in a traveling harmonic wave, we need to compare the phase angles of the wave at those points.In the given wave equation, the phase angle is represented by the term inside the cosine function, i.e., 2\u03c0(wt - kx + 0.35), where w represents the angular frequency and k represents the wave number.Let's assume the two points are at x1 and x2, separated by a distance \u0394x = x2 - x1. The phase difference between the oscillatory motion of these two points can be calculated using the equation: Phase difference = 2\u03c0(k\u0394x)"
    },
    {
        "instruction": "The volume of 80 g of a substance is 188 cm\u00b3. If the density of the liquid in which the substance is placed is 9 g/cm\u00b3, will the substance float or sink?",
        "input": "Density of Substance = 0.425531914893617 g/cm\u00b3, Density of Liquid = 9 g/cm\u00b3",
        "output": "The substance will float."
    },
    {
        "instruction": "Two stars each of one solar mass 74000000000000000000000000000000 kg are approaching each other for a head-on collision. When they are at a distance 40000000000 km, their speeds are negligible. What is the speed with which they collide? The radius of each star is 310000 km. Assume the stars remain undistorted until they collide.",
        "input": "Speed = sqrt((-G*m/R) + (G*m/(2*r))) = sqrt(((-6.67 * 10^-11) * 74000000000000000000000000000000) / (40000000000000)) + ((6.67 * 10^-11) * 74000000000000000000000000000000) / (620000000))",
        "output": "The speed with which the stars collide is approximately 2.82e+06 m/s."
    },
    {
        "instruction": "Two balls each of mass 1031 g, moving in opposite directions with speed 1171 m/s collide and rebound with the same speed. What is the impulse imparted to each ball due to the other?",
        "input": "Impulse calculation",
        "output": "2414.6\nThe impulse imparted to each ball due to the other can be calculated using the formula (2 * mass * velocity) / 1000, where the mass is 1031 g and the velocity is 1171 m/s. The result is 2414.6 kg\u00b7m/s, in the direction of the final velocity for both balls."
    },
    {
        "instruction": "A series LCR circuit is connected to a variable frequency 230 V source with L = 127 H, C = 49 muF, R = 23 ohm. Determine the impedance of the circuit at the resonating frequency?",
        "input": "Impedance = sqrt(R^2 + (\u03c9L - 1 / (\u03c9C))^2)",
        "output": "23 ohm"
    },
    {
        "instruction": "In a harbour, wind is blowing at the speed of 2047 m/s and the flag on the mast of a boat anchored in the harbour flutters along the N-E direction. If the boat starts moving at a speed of 1303 m/s to the north, what is the direction of the flag on the mast of the boat?",
        "input": "v1 = 2047 m/s, v2 = 1303 m/s",
        "output": "6 degrees north of east"
    },
    {
        "instruction": "A charge of 4 mC is located at the origin. Calculate the work done in taking a charge 6 nC from a point P(16 cm, 0, 0) to a point Q(1 cm, 0, 0), via a point R(17 cm, 0, 20 cm).",
        "input": "Charge at Origin (q1) = 4 mC + Charge at P (q2) 6 nC + Coordinates of P: (16 cm, 0, 0) + Coordinates of Q : (1 cm, 0, 0) + Coordinates of R : (17 cm, 0, 20 cm)",
        "output": "2.02e-01 joule\nExplanation: The work done in moving a charge between two points is given by the formula W = q1 * q2 * (Vp - Vq), where q1 and q2 are the charges, and Vp and Vq are the potentials at the respective points. The potential difference (Vp - Vq) is calculated as 0.009 * (1 / p - 1 / q). Plugging in the values, we get W = 2.02e-01 joule."
    },
    {
        "instruction": "A charge of 11 mC is located at the origin. Calculate the work done in taking a charge 12 nC from a point P(1 cm, 0, 0) to a point Q(0, 0, 13 cm), via a point R(1 cm, 4 cm, 0).",
        "input": "Charge at Origin (q1) = 11 mC + Charge at P (q2) 12 nC + Coordinates of P: (1 cm, 0, 0) + Coordinates of Q : (0, 0, 13 cm) + Coordinates of R : (1 cm, 4 cm, 0)",
        "output": "1.10e+00 joule\nExplanation: The work done in moving a charge between two points is given by the formula W = q1 * q2 * (Vp - Vq), where q1 and q2 are the charges, and Vp and Vq are the potentials at the respective points. The potential difference (Vp - Vq) is calculated as 0.009 * (1 / p - 1 / q). Plugging in the values, we get W = 1.10e+00 joule."
    },
    {
        "instruction": "A body is dropped from the top of a building with an initial velocity of 2568 m/s under gravity, and it reaches the ground after 79 s. What is the height of the building?",
        "input": "initial velocity (u) = 2568 m/s, time (t) = 79 s",
        "output": "height (s) = initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)\u00b2\ns = 2568 * 79 + 0.5 * 9.8 * 79\u00b2\ns = 202872 + 30580.9\ns = 233452.9"
    },
    {
        "instruction": "A meter stick of mass 9 g is balanced on a knife edge at its center. When a coin is put at the 39 mark, the stick is found to be balanced at 82 cm. What is the mass of the meter stick?",
        "input": "Mass = (Right Side) / Distance",
        "output": "The mass of the meter stick is approximately -35.2 g.\nRight Side = m * (t - t1) = 9 * (82 - 39)"
    },
    {
        "instruction": "Two gold pieces of masses are 59600.07 g and 500.0071 g respectively. What is the sum of the masses of the pieces to correct significant figures?\n",
        "input": "",
        "output": "6.010008e+04\n"
    },
    {
        "instruction": "If a force of -8i + -9j + 9k N acts on a body and displaces it 26 m in the direction of x, 38 m in the direction of y, and 40 m in the direction of z, then what is the work done by the force on the body?",
        "input": "Work = (x * sx) + (y * sy) + (z * sz)",
        "output": "To calculate the work done, we use the formula Work = (x * sx) + (y * sy) + (z * sz), where x, y, and z are the components of the force (in N) along the x, y, and z directions, respectively, and sx, sy, and sz are the displacements (in m) in the corresponding directions., this is the final answer -190"
    },
    {
        "instruction": "A double convex lens has radii of curvatures 3 cm and 100 cm, and is made of material with a refractive index of 1.16. What is the focal length of the lens?",
        "input": "Formula: f = 1 / ((mu - 1) * ((1 / r1) - (1 / r2)))",
        "output": "To find the focal length of the double convex lens, we use the formula f = 1 / ((mu - 1) * ((1 / r1) - (1 / r2))), where f is the focal length, mu is the refractive index of the lens material, r1 is the radius of curvature of the first surface, and r2 is the radius of curvature of the second surface. By substituting the given values into the formula, we can solve for f. In this case, the focal length of the lens is 18.2 cm., this is the final The focal length of the lens is 18.2 cm."
    },
    {
        "instruction": "Two objects of masses 1 g and 11 g are moving along the same line and direction with velocities of 7 m/s and 25 m/s respectively. They collide and after the collision, the second object moves at a velocity of 26 m/s. Determine the initial velocity of the second object.",
        "input": "u2 = ((m1 * v1) + (m2 * v2) - (m1 * u1)) / m2",
        "output": "To find the initial velocity of the second object (u2), we use the formula:\n\nu2 = ((m1 * v1) + (m2 * v2) - (m1 * u1)) / m2\n\nSubstituting the given values, we have:\n\nu2 = ((1 * 26) + (11 * 6) - (1 * 7)) / 11\n\nSimplifying the expression gives us u2 = 7.7 m/s."
    },
    {
        "instruction": "What is the gravitational potential at a point P at a distance of 324 m from a mass of 17 kg?",
        "input": "Gravitational Potential (V) = cal3(17, 324) joule/kg",
        "output": "The gravitational potential at a point P at a distance of 324 m from a mass of 17 kg is given by the formula V = (-G * m) / r, where G is the gravitational constant, m is the mass, and r is the distance. Plugging in the values, we get V = -3.50e-12 joule/kg."
    },
    {
        "instruction": "Number of significant digits in 0.1078490\n",
        "input": "",
        "output": "0 zeros after the decimal point to the left of first non zero digit are not significant, 6 digits(which start and end with non zero digit) in between are significant, 1 digits to the right of last non-zero digits are significant(as they are after decimal point), in total 6 + 1 = 7 digits are significant.\n"
    },
    {
        "instruction": "If the position of the particle is given by r = (6*t**4) i + (-t**3) j + (8*t**2) k m, where t is in seconds, what is the acceleration of the particle (in vector notation)?",
        "input": "r = xi + yj + zk, v = dr/dt, a = dv/dt",
        "output": "The acceleration of the particle is (72*t**2) i + (-6*t) j + (16) k m/s^2."
    },
    {
        "instruction": "A rectangular wire loop of sides 4 cm and 1 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 2.0 T directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is 54 cm/s in a direction normal to the two different sides of the loop? For how long does the induced voltage last in each case?\n",
        "input": "EMF = B * l * v",
        "output": "4.32e-02 volt for 7.41e-02 s if the velocity is perpendicular to the 4 cm side, 1.08e-02 volt for 1.85e-02 s if the velocity is perpendicular to the 1 cm side\n\n\nThe electromotive force (EMF) can be calculated using the formula EMF = B * l * v, where B is the magnetic field magnitude, l is the side length of the rectangular wire loop, and v is the velocity of the loop after conversion from cm/s to m/s."
    },
    {
        "instruction": "A convex mirror produces a real image of height 497 cm of a real object of height 709 cm placed in front of it. What is the magnification of the mirror?",
        "input": "Formula: m = hi / ho = v / u",
        "output": "To find the magnification of the convex mirror, we use the formula m = hi / ho = v / u, where m is the magnification, hi is the height of the image, ho is the height of the object, v is the distance of the image from the mirror, and u is the distance of the object from the mirror. Since the heights are provided instead of distances, the formula still holds. By substituting the given values into the formula, we can calculate the magnification. In this case, the magnification of the mirror is 0.7., this is the final The magnification of the mirror is 0.7."
    },
    {
        "instruction": "A solenoid of magnetic moment 0.76 J/T is kept in a uniform magnetic field of 0.36 T. What is the work done by an external torque to turn the magnet which is aligned at an angle of 86 degrees with the magnetic field to an angle of 146 degrees?",
        "input": "-m * b * (d1 - d2)",
        "output": "The work done by an external torque to turn the magnet aligned at an angle of 0.06975647374412546 degrees with the magnetic field to an angle of -0.8290375725550416 degrees can be calculated using the formula -m * b * (d1 - d2), where 'm' is the magnetic moment of the magnet, 'b' is the magnetic field strength, 'd1' is the initial angle, and 'd2' is the final angle. Substituting the given values, we have -(0.76) * 0.36 * (0.07 - -0.83)."
    },
    {
        "instruction": "Two circular coils X and Y of radii 31 cm and 12 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil A has 11 turns and carries a current of 12 A, Coil B has 7 turns and carries a current of 19 A. The sense of current in X is anti-clockwise direction and in Y is clockwise direction. From an observer looking at the coils facing east, give the magnitude and direction of the net magnetic field due to the coils at the center.",
        "input": "Net magnetic field = |b1 - b2|",
        "output": "To calculate the net magnetic field, we use the following formula:\n\nNet magnetic field = |b1 - b2|\n\nWhere,\n- b1 = Magnetic field due to coil X\n- b2 = Magnetic field due to coil Y\n\nWe calculate the magnetic field for each coil using the formula:\n- Magnetic field due to coil X = (mu * n1 * i1) / (2 * r1)\n- Magnetic field due to coil Y = (mu * n2 * i2) / (2 * r2)\n\nSubstituting the given values and evaluating the formula, we find that the magnitude of the net magnetic field is approximately 4.29e-04 tesla and towards west."
    },
    {
        "instruction": "An image is formed by a convex lens of focal length 492 cm at a distance of 520 cm behind it. Find at what distance object is placed in front of lens.",
        "input": "Formula: 1/f = 1/v - 1/u for convex lens.",
        "output": "To find the distance of the object from the lens, we use the formula for convex lenses: 1/f = 1/v - 1/u, where f is the focal length ofthe lens, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 9137.1 cm from the lens., this is the final The object is placed at 9137.1 cm in front of the lens."
    },
    {
        "instruction": "A 186 cm long metallic rod is rotated with an angular frequency of 123 rad s-1 about an axis normal to the rod passing through one of its ends. The other end of the rod is in contact with a circular metallic ring. A uniform magnetic field of 60 T parallel to the axis exists everywhere. Find the EMF developed between the center and the ring.\n",
        "input": "EMF = (B * l * w^2) / 2",
        "output": "8.44e+07 volt\n\n\nThe electromotive force (EMF) can be calculated using the formula EMF = (B * l * w^2) / 2, where B is the magnetic field magnitude, l is the length of the metallic rod, and w is the angular frequency of rotation in radians per second."
    },
    {
        "instruction": "Torque of 25 Nm is transmitted to an engine at a power of 547 W. What is the angular speed of the rotor?",
        "input": "Angular Speed = Power / Torque",
        "output": "Angular Speed = 547 W / 25 Nm\n\nTo calculate the angular speed of the rotor, we use the following formula:\n\nAngular Speed = Power / Torque\n\nSubstituting the values:\n\nPower = 547 W\nTorque = 25 Nm\n\nWe find that the angular speed of the rotor is 21.9 rad/s."
    },
    {
        "instruction": "A solenoid of magnetic moment 1.99 J/T is kept in a uniform magnetic field of 0.71 T. What is the work done by an external torque to turn the magnet which is aligned at an angle of 45 degrees with the magnetic field to an angle of 179 degrees?",
        "input": "-m * b * (d1 - d2)",
        "output": "The work done by an external torque to turn the magnet aligned at an angle of 0.7071067811865476 degrees with the magnetic field to an angle of -0.9998476951563913 degrees can be calculated using the formula -m * b * (d1 - d2), where 'm' is the magnetic moment of the magnet, 'b' is the magnetic field strength, 'd1' is the initial angle, and 'd2' is the final angle. Substituting the given values, we have -(1.99) * 0.71 * (0.71 - -1.00)."
    },
    {
        "instruction": "An electron is projected between parallel plates separated by 1.0 cm, having a field of 900 N/C (up to down), with a speed of 780000 m/s. In what time will the electron strike the upper plate?\n",
        "input": "Time Taken Formula: time_taken = sqrt(2 * d * 0.01 * 9.1 * 10^(-31) * v^2 / (1.6 * 10^(-19) * E))\n",
        "output": "8.77e-03 s\n"
    },
    {
        "instruction": "A sound wave travels at a speed of 605856.5 m/s, if it's wavelength is 37 m, will the sound wave be audible ? \n",
        "input": "frequency = wave speed / wavelength",
        "output": "audible\nWhether a sound wave is audible or not depends on its frequency, not its wavelength. Audible sound waves have frequencies within the range of human hearing, which is typically between 20 Hz and 20,000 Hz. To determine if a sound wave is audible, we need to calculate its frequency using the wave speed and wavelength. The formula to calculate the frequency of a sound wave is: f = v / \u03bb, where f is the frequency, v is the wave speed, and \u03bb is the wavelength. Substituting the given values into the formula, we can calculate the frequency of the sound wave: f = 605856.5 m/s / 37 m. Now, we can compare the calculated frequency to the audible frequency range (20 Hz to 20,000 Hz) to determine if the sound wave is audible or not."
    },
    {
        "instruction": "A long straight wire in the horizontal plane carries a current of of 342 A in west to east direction. What is the magnitude and direction of the magnetic field B at a point 1136 cm north of the wire. (mu = 4 x pi x 10-7 TmA-1)\n",
        "input": "B = (mu * i) / (2 * pi * r)",
        "output": "To calculate the magnitude and direction of the magnetic field B, we use the following formula:\n\nB = (mu * i) / (2 * pi * r)\n\nWhere,\n- B = Magnetic field\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- i = Current flowing through the wire\n- r = Distance from the wire\n\nSubstituting the given values into the formula, we find that the magnitude and direction of the magnetic field B is approximately 6.0e-06 tesla vertically upwards\n."
    },
    {
        "instruction": "What is the gravitational field at a point P at a distance of 89 m from a mass of 488 kg?",
        "input": "Gravitational Field (g) = cal3(488, 89) N/kg",
        "output": "The gravitational field at a point P at a distance of 89 m from a mass of 488 kg is given by the formula g = (-G * m) / (r^2), where G is the gravitational constant, m is the mass, and r is the distance. Plugging in the values, we get g = -4.11e-12 N/kg."
    },
    {
        "instruction": "An Electric Iron of resistance 48 ohm takes a current of 10 A, then what is the heat developed in 38 s?",
        "input": "Heat = I^2 * R * t",
        "output": "To calculate the heat developed in the Electric Iron, we use the formula Heat = I^2 * R * t, where I is the current (10 A), R is the resistance (48 ohm), and t is the time (38 s)., this is the final answer 182400"
    },
    {
        "instruction": "A series LCR circuit is connected to a variable frequency 230 V source with L = 37 H, C = 103 muF, R = 6 ohm. Determine the RMS potential drop across capacitance?",
        "input": "RMS Potential Drop across Capacitance = Current RMS * 1 / (\u03c9_r * C)",
        "output": "2.30e+04 volt"
    },
    {
        "instruction": "What is the highest total resistance that can be secured by combinations of three coils of resistance 110, 125, 85?",
        "input": "R_total = R1 + R2 + R3",
        "output": "The highest combination of resistances can be obtained by connecting them in series. The total resistance is 110 + 125 + 85 = 320 ohm.\n\nTo calculate the highest combination of resistances, we add the resistances in series. The total resistance (R_total) is equal to the sum of the individual resistances (R1, R2, and R3)."
    },
    {
        "instruction": "Calculate the charge (in C) of 1.69e+18 electrons?",
        "input": "Q = n * e",
        "output": "3.00e-01 coulomb\n\nThe charge of electrons can be calculated using the formula: Q = n * e, where n is the number of electrons and e is the charge of an electron."
    },
    {
        "instruction": "A spring balance has a scale that reads from 0 to 122 kg. The length of the scale is 52 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 520 ms. What is the weight of the body?",
        "input": "Formula: w = (t^2 * k) / (4 * \u03c0^2), where w is the weight of the body, t is the period of oscillation (520 ms), and k is the spring constant given by (m * g) / (l * 0.01), where m is the reading on the scale (122 kg), g is the acceleration due to gravity (9.8 m/s^2), and l is the length of the scale (52 cm).",
        "output": "Using this formula: Formula: w = (t^2 * k) / (4 * \u03c0^2), where w is the weight of the body, t is the period of oscillation (520 ms), and k is the spring constant given by (m * g) / (l * 0.01), where m is the reading on the scale (122 kg), g is the acceleration due to gravity (9.8 m/s^2), and l is the length of the scale (52 cm)., this is the final answer derived: The spring constant k can be found out using the maximum mass and length of the scale as k = (m * g) / (l * 0.01), which is (122 * 9.8) / (0.52) = 2299.23.\nWe know that the time period of simple harmonic motion is given by t = 2\u03c0\u221a(m / k). From this equation, we can rearrange it to solve for m: m = (t^2 * k) / (4\u03c0^2).\nMultiplying the resulting mass with g, we get the weight, which is equal to (520^2 * 2299.23) / (4\u03c0^2) = 1.54e+02 newton."
    },
    {
        "instruction": "A solid cylinder of mass 6207 kg has a radius of 48 m and length of 88 m. What is the moment of inertia with respect to its diameter?",
        "input": "Moment of Inertia = (Constant1) * mass * length^2 + (Constant2) * mass * radius^2",
        "output": "The moment of inertia with respect to its end is approximately 4005584.0 kgm^2.\n\nMoment of Inertia = (Constant1) * mass * length^2 + (Constant2) * mass * radius^2\n\nConstant1 = 0.08333333333333333\nConstant2 = 0.5\nmass = 6207 kg\nlength = 88 m\nradius = 48 m"
    },
    {
        "instruction": "A rope of negligible mass is wound round a hollow sphere of mass 47 kg and radius 73 cm. What is the linear acceleration of the hollow sphere if the rope is pulled with a force of 12 N? Assume that there is no slipping.",
        "input": "Acceleration = Force / (k * mass * radius)",
        "output": "Acceleration = 12 N / (0.6666666666666666 * 47 kg * 73 cm)\n\nTo calculate the linear acceleration of the hollow sphere, we use the following formula:\n\nAcceleration = Force / (k * mass * radius)\n\nSubstituting the values:\n\nForce = 12 N\nk = 0.6666666666666666\nMass = 47 kg\nRadius = 73 cm\n\nWe find that the linear acceleration of the hollow sphere is approximately 0.4 m/s\u00b2."
    },
    {
        "instruction": "A double concave lens has radii of curvatures 8 cm and 56 cm, and is made of material with a refractive index of 1.42. What is the focal length of the lens?",
        "input": "Formula: f = 1 / ((mu - 1) * ((1 / r1) - (1 / r2)))",
        "output": "To find the focal length of the double concave lens, we use the formula f = 1 / ((mu - 1) * ((1 / r1) - (1 / r2))), where f is the focal length, mu is the refractive index of the lens material, r1 is the radius of curvature of the first surface, and r2 is the radius of curvature of the second surface. By substituting the given values into the formula, we can solve for f. In this case, the focal length of the lens is -16.67 cm., this is the final The focal length of the lens is -16.67 cm."
    },
    {
        "instruction": "A stone is thrown vertically upward and reaches a maximum height of 247602 m. What is the initial velocity of the stone?",
        "input": "maximum height (h) = 247602 m",
        "output": "maximum height (h) = (initial velocity (u)\u00b2) / (2 * acceleration (g))\n247602 = (u\u00b2) / (2 * 9.8)\n247602 = u\u00b2 / 19.6\n247602 * 19.6 = u\u00b2\n4852999.2 = u\u00b2\n\u221a4852999.2 = u\nu = 2203.0"
    },
    {
        "instruction": "A hollow cylinder of radius 393 m weighs 29 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 4 m/s. How much work has to be done to stop it?\n",
        "input": "0.5*(1+1)*m*v*v",
        "output": "464.0 joules\n"
    },
    {
        "instruction": "Find the ratio of time taken by the sound wave to travel a distance of 4 m in material-1 and material-2 (speed of sound in material-1 is 1654 m/s, in material-2 is 8407 m/s) ?\n",
        "input": "Speed = Distance/Time",
        "output": "5.1\nTo find the ratio of the time taken by the sound wave to travel a distance of 4 m in material-1 and material-2, we can use the equation: Ratio of time = time in material-1 / time in material-2. The time taken by the sound wave to travel a distance in material-1 can be calculated using the equation: time in material-1 = distance / speed in material-1. Similarly, the time taken by the sound wave to travel the same distance in material-2 can be calculated using: time in material-2 = distance / speed in material-2. Substituting the given values into the equations, we have: time in material-1 = 4 m / 1654 m/, time in material-2 = 4 m / 8407 m/s. Therefore, the ratio of the time taken by the sound wave to travel a distance of 4 m in material-1 and material-2 is: Ratio of time = (4 m / 1654 m/s) / (4 m / 8407 m/s)= 5.082829504232165"
    },
    {
        "instruction": "An Electric motor takes 7 A current, if it consumes 224 J of energy in 35 s, then determine potential difference?",
        "input": "V = Energy / (I * t)",
        "output": "To calculate the potential difference, we use the formula V = Energy / (I * t), where Energy is the energy consumed (224 J), I is the current (7 A), and t is the time (35 s)., this is the final answer 0.9"
    },
    {
        "instruction": "The edge of a cube is 182 cm long. One face of the cube is firmly fixed to a vertical wall. A mass of 69 kg is then attached to the opposite face of the cube. The shear modulus of the material of the cube is 159 GPa. What is the vertical deflection of this face?",
        "input": "deflection = (mass * 9.8) / (Y * 10^9 * (edge_length * 10^-2))",
        "output": "To calculate the vertical deflection, we use the formula:\n\ndeflection = (mass * 9.8) / (Y * 10^9 * (edge_length * 10^-2))\n   = (69 kg * 9.8) / (159 * 10^9 GPa * (182 cm * 10^-2 m/cm))\n   = 2.3 nm."
    },
    {
        "instruction": "A stone tied to the end of a string 173 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 220 revolutions in 147 s, what is the magnitude and direction of acceleration of the stone?",
        "input": "a = v\u00b2/r, v = 2\u03c0r/T",
        "output": "a = 153.0 ms-2, towards the centre of the circle, v = 9.4 rad/s\n {explanation}}"
    },
    {
        "instruction": "What is the potential energy of an object of mass 889 kg placed at a height 718 m?",
        "input": "PE = m * g * h",
        "output": "To calculate the potential energy, we use the formula PE = m * g * h, where PE is the potential energy, m is the mass (889 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height (718 m)., this is the final answer 6255359.6"
    },
    {
        "instruction": "What is the number of photons of light with wavelength 313409 pm which provide 38 Joule of energy ? \n",
        "input": "Number of photons = Energy*wavelength/h*c",
        "output": "6.01e+19\nTo find the number of photons of light with a given wavelength and energy, we can use the equation: Number of photons = Energy / Energy of each photonTo calculate the energy of each photon, we can use the formula: Energy of each photon = h * c / \u03bb, where h is the Planck constant (approximately 6.626 x 10^-34 J\u00b7s), c is the speed of light (approximately 3 x 10^8 m/s), and \u03bb is the wavelength of light in meters."
    },
    {
        "instruction": "If a diatomic gas of 8 moles at 20 pas is isothermally changed to pressure 58 pas at 36 K, then what is the work done.\n",
        "input": "Work Done = n*R*T*ln(P1/P2)",
        "output": "2548.2 joules\nTo calculate the work done during an isothermal expansion of a diatomic gas, we can use the following equation: Work done = n * R * T * ln(P1/P2), where n is the number of moles of the gas, R is the ideal gas constant (approximately 8.314 J/(mol\u00b7K)), T is the temperature in Kelvin, P1 is the initial pressure, and P2 is the final pressure."
    },
    {
        "instruction": "An object is placed at 10 cm in front of a concave mirror. Image is formed at a distance of 339 cm in front of it. Find the focal length of the mirror.",
        "input": "Formula: 1/f = 1/v + 1/u",
        "output": "To find the focal length of the mirror, we use the formula 1/f = 1/v + 1/u, where f is the focal length, v is the distance of the image, and u is the distance of the object. By substituting the given values into the formula, we can solve for f. In this case, the focal length of the mirror is 9.7 cm., this is the final 9.7"
    },
    {
        "instruction": "A bullet of mass 67 kg and horizontal speed 44 m/s strikes a block of wood of mass 40 kg and instantly comes to rest with respect to the block. The block is suspended from the ceiling by a thin wire. Calculate the height to which the block rises.",
        "input": "h = (v^2) / (2 * g)",
        "output": "To calculate the height, we use the formula h = (v^2) / (2 * g), where h is the height, v is the velocity of the bullet after the collision, and g is the acceleration due to gravity (9.8 m/s^2)., this is the final answer 38.7"
    },
    {
        "instruction": "If a force of -9i + -4j + -8k N acts on a body and displaces it 7 m in the direction of x, 39 m in the direction of y, and 29 m in the direction of z, then what is the work done by the force on the body?",
        "input": "Work = (x * sx) + (y * sy) + (z * sz)",
        "output": "To calculate the work done, we use the formula Work = (x * sx) + (y * sy) + (z * sz), where x, y, and z are the components of the force (in N) along the x, y, and z directions, respectively, and sx, sy, and sz are the displacements (in m) in the corresponding directions., this is the final answer -451"
    },
    {
        "instruction": "A long straight wire in the horizontal plane carries a current of of 454 A in north to south direction. What is the magnitude and direction of the magnetic field B at a point 965 cm east of the wire.\n",
        "input": "B = (mu * i) / (2 * pi * r)",
        "output": "To calculate the magnitude and direction of the magnetic field B, we use the following formula:\n\nB = (mu * i) / (2 * pi * r)\n\nWhere,\n- B = Magnetic field\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- i = Current flowing through the wire\n- r = Distance from the wire\n\nSubstituting the given values into the formula, we find that the magnitude and direction of the magnetic field B is approximately 9.4e-06 tesla vertically upwards\n."
    },
    {
        "instruction": "A meter stick of mass 80 g is balanced on a knife edge at its center. Where will the stick be balanced when a coin of mass 92 g is put at the 28 mark?",
        "input": "Balance Position = ((50 * m) + (m1 * t1)) / (m + m1)",
        "output": "The stick will be balanced at approximately 38.2 cm.\nBalance Position = ((50 * 80) + (92 * 28)) / (80 + 92)"
    },
    {
        "instruction": "A body is dropped from a height of 4926 m with an initial velocity of 60 m/s. With what velocity will it strike the ground?",
        "input": "height (h) = 4926 m, initial velocity (u) = 60 m/s",
        "output": "final velocity (v) = \u221a(initial velocity (u)\u00b2 + 2 * acceleration (g) * height (h))\nv = \u221a(60\u00b2 + 2 * 9.8 * 4926)\nv = \u221a(3600 + 96549.6)\nv = \u221a100149.6\nv = \u221a316.5\nv = 316.5"
    },
    {
        "instruction": "A bat emits ultrasonic sound of frequency 1769598 Hz in air. If this sound meets a water surface, what is the wavelength of the reflected sound? (Speed of sound in air = 340 ms-1 and in water = 1486 ms-1)\n",
        "input": "wavelength of refracted sound = speed of sound in air/frequency of the ultrasonic sound",
        "output": "1.92e-04 m\nGiven that the speed of sound in air is 340 m/s and the speed of sound in water is 1486 m/s, we can substitute these values into the formula to calculate the wavelength. For the sound emitted in air: \u03bb_air = (340 m/s) / 1769598 Hz, For the sound reflected in water: \u03bb_water = (1486 m/s) / 1769598 Hz"
    },
    {
        "instruction": "A series LCR circuit is connected to a variable frequency 230 V source with L = 180 H, C = 36 muF, R = 121 ohm. Determine the RMS potential drop across capacitance?",
        "input": "RMS Potential Drop across Capacitance = Current RMS * 1 / (\u03c9_r * C)",
        "output": "4.25e+03 volt"
    },
    {
        "instruction": "Two spheres q1 of charge 46 x 10^(-6)C, q2 of charge 147 x 10^(-6)C are placed at a distance 121 cm. If an uncharged sphere C first comes in contact with A, then with B and placed at 121 cm from both of them, then what is the final force between A and C?\n",
        "input": "Final force between A and C = k * qa * qb / d^2",
        "output": "The final force between spheres A and C can be calculated using the formula F = k * qa * qb / d^2, where k is the electrostatic constant, qa and qb are the charges on A and C respectively, and d is the distance between them. Therefore, the final force between A and C is 1.20e+01 newton\n"
    },
    {
        "instruction": "A transverse harmonic wave on a string is described by y(x, t) = 5 sin (30 t + 0.126 x + \u03c0/5) where x and y are in cm and t in s. The positive direction of x is from left to right, then what is the initial phase at the origin?\n",
        "input": "frequency = speed/wavelength",
        "output": "\u03c0/5\nTo determine the initial phase, we look at the phase term in the equation, which is \"+str(k)+\"x + \u03c0/\"+str(div)+\". At the origin (x=0), the phase term becomes \"+str(\"\u03c0/\"+str(div))+\". Hence, the initial phase at the origin is \"+str(\"\u03c0/\"+str(div))+\" radians or \"+str(\"180/\"+str(div))+\" degrees."
    },
    {
        "instruction": "A 19 ohm resistor is connected to a 105 V, 135 Hz ac supply. What is the net power consumed over a full cycle?",
        "input": "P_net = (V ** 2) / R",
        "output": "5.80e+02 watt"
    },
    {
        "instruction": "A closely wounded solenoid 229 cm long has 3 layers of windings of 300 turns each. The diameter of the solenoid is d cm. If the current carried is 45 A, estimate the magnitude of the magnetic field inside the solenoid near its center.",
        "input": "B = (mu * n * i) / l",
        "output": "To estimate the magnitude of the magnetic field inside the solenoid near its center, we use the following formula:\n\nB = (mu * n * i) / l\n\nWhere,\n- B = Magnetic field inside the solenoid near its center\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- n = Number of turns per layer\n- i = Current flowing through the solenoid\n- l = Length of the solenoid\n\nSubstituting the given values into the formula, we find that the magnitude of the magnetic field inside the solenoid near its center is approximately 7.41e-03 tesla."
    },
    {
        "instruction": "A police van moving on a highway with a speed of 143 m/s fires a bullet at a thief's car speeding away in the same direction with a speed of 319 m/s. If the muzzle speed of the bullet is 1148 m/s, with what speed does the bullet hit the thief's car?",
        "input": "v1 = 143 m/s, v2 = 319 m/s, v3 = 1148 m/s",
        "output": "The speed of the bullet is 1291 m/s, and the relative speed of the bullet with respect to the thief's car is 972 m/s"
    },
    {
        "instruction": "A helicopter of mass 1246 kg rises with a vertical acceleration of 2 m/s^2. The crew and the passengers weigh 319 kg. Give the magnitude and direction of",
        "input": "force on the floor by the crew and passengers",
        "output": "3828 newton, vertically downwards\n\nThe force on the floor by the crew and passengers can be calculated based on the given mass (1246 kg), weight of crew and passengers (319 kg), and acceleration (2 m/s^2)."
    },
    {
        "instruction": "A circuit consists of 17 V battery, 193 ohm resistance, then what is the time taken to produce 907 J of energy in the circuit?",
        "input": "t = (energy * R) / (V^2)",
        "output": "To calculate the time taken, we rearrange the formula t = (energy * R) / (V^2) to solve for t. Substituting the values, where energy is 907 J, R is 193 ohm, and V is 17 V, we can calculate the time., this is the final answer 605.7"
    },
    {
        "instruction": "The volume of 1055 g of a substance is 129 cm\u00b3. If the density of the liquid in which the substance is placed is 5 g/cm\u00b3, will the substance float or sink?",
        "input": "Density of Substance = 8.178294573643411 g/cm\u00b3, Density of Liquid = 5 g/cm\u00b3",
        "output": "The substance will sink."
    },
    {
        "instruction": "Calculate the enthalpy change on freezing of 17 mol of water at 11.5 celcius to ice at -57.5 celcius.\n",
        "input": "(\u0394H)=(\u0394H1)+(\u0394H2)",
        "output": "81258.3\nTotal enthalpy change involved in the transformation is the sum of the following changes and can be represented using the Hess Law."
    },
    {
        "instruction": "What is the number of photons of light with wavelength 899095 pm which provide 1 Joule of energy ? \n",
        "input": "Number of photons = Energy*wavelength/h*c",
        "output": "4.54e+18\nTo find the number of photons of light with a given wavelength and energy, we can use the equation: Number of photons = Energy / Energy of each photonTo calculate the energy of each photon, we can use the formula: Energy of each photon = h * c / \u03bb, where h is the Planck constant (approximately 6.626 x 10^-34 J\u00b7s), c is the speed of light (approximately 3 x 10^8 m/s), and \u03bb is the wavelength of light in meters."
    },
    {
        "instruction": "An object moving with a speed of 457 kmph covers x m in 83 s, then find the value of x?\n",
        "input": "Distance = Speed*Time",
        "output": "10536.4\nDistance = Speed*Time"
    },
    {
        "instruction": "What is the pressure inside a drop of liquid of radius 3 mm at room temperature? Surface tension of liquid at that temperature (262 K) is 573 x 10^(-3) Nm^(-1). Also give the excess pressure inside the drop.",
        "input": "excess pressure = (2 * surface tension) / radius, total pressure = 1.01 * (10 ** 5) + excess pressure",
        "output": "The excess pressure inside the drop is 382.00 pascal. The total pressure inside the drop is 1.01e+05 pascal."
    },
    {
        "instruction": "Suppose there existed a planet that went around the Sun 1827/595 times as fast as the Earth. What would be its orbital size as compared to that of the Earth?",
        "input": "Orbital Size Ratio = (T_p / T_e)^(2/3) = (1827/595)^(2/3)",
        "output": "The orbital size of the planet compared to that of the Earth would be approximately 2.1 times faster than Earth."
    },
    {
        "instruction": "A convex mirror produces 47 times diminished real image of height 0.31 cm of an object placed in front of it. What is the height of the object taken?",
        "input": "Formula: ho = hi * n",
        "output": "To find the height of the object taken in front of the convex mirror, we use the formula ho = hi * n, where ho is the height of the object, hi is the height of the image, and n is the magnification factor. By substituting the given values into the formula, we can calculate ho. In this case, the height of the object taken in front of the convex mirror is 14.6 cm., this is the final The height of the object taken in front of the convex mirror is 14.6 cm."
    },
    {
        "instruction": "A TV antenna is 5731 cm tall. How much service area can it cover if the receiving antenna is at ground level?",
        "input": "Service_area = pi * 2 * 6.4 * 10000 * l",
        "output": "2.30e+09 m2"
    },
    {
        "instruction": "Two large thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude 1630036 x 10^(-22) C/m\u00b2. What is E: between the plates?\n",
        "input": "Electric field (E) = surface charge density / (2 * epsilon_0)",
        "output": "To calculate the electric field between the plates, we use the formula:\nElectric field (E) = surface charge density / (2 * epsilon_0)\nGiven surface charge density = 1630036 x 10^(-22) C/m\u00b2,\nElectric field (E) = 1.84e-05 N/C\n"
    },
    {
        "instruction": "Two circular coils X and Y of radii 24 cm and 29 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil A has 10 turns and carries a current of 14 A, Coil B has 15 turns and carries a current of 17 A. The sense of current in X is anti-clockwise direction and in Y is clockwise direction. From an observer looking at the coils facing east, give the magnitude and direction of the net magnetic field due to the coils at the center.",
        "input": "Net magnetic field = |b1 - b2|",
        "output": "To calculate the net magnetic field, we use the following formula:\n\nNet magnetic field = |b1 - b2|\n\nWhere,\n- b1 = Magnetic field due to coil X\n- b2 = Magnetic field due to coil Y\n\nWe calculate the magnetic field for each coil using the formula:\n- Magnetic field due to coil X = (mu * n1 * i1) / (2 * r1)\n- Magnetic field due to coil Y = (mu * n2 * i2) / (2 * r2)\n\nSubstituting the given values and evaluating the formula, we find that the magnitude of the net magnetic field is approximately 1.86e-04 tesla and towards west."
    },
    {
        "instruction": "A force is applied on a body of mass 980 kg placed on a smooth surface resulting in acceleration of 133 m/s^2, then what is the force applied?",
        "input": "F = m * a",
        "output": "130340\nTo calculate the force, we use the formula F = m * a, where F is the force, m is the mass (980 kg), and a is the acceleration (133 m/s^2)."
    },
    {
        "instruction": "A 9410 N force is applied on a body placed on a smooth surface resulting in acceleration of 761 m/s^2, then what is the mass of the body?",
        "input": "m = F / a",
        "output": "12.4\nTo calculate the mass, we use the formula m = F / a, where m is the mass, F is the force (9410 N), and a is the acceleration (761 m/s^2)."
    },
    {
        "instruction": "A concave lens produces a real image of height 94 cm at a distance of 47 cm from it of a real object placed 119 cm in front of it. What is the height of the object?",
        "input": "Formula: ho = (hi * u) / v",
        "output": "To find the height of the object, we use the formula ho = (hi * u) / v, where ho is the height of the object, hi is the height of the image, u is the distance of the object from the lens, and v is the distance of the image from the lens. By substituting the given values into the formula, we can solve for ho. In this case, the height of the object is 238.0 cm., this is the final The height of the object is 238.0 cm."
    },
    {
        "instruction": "A transverse harmonic wave on a string is described by y(x, t) = 42 sin (82 t + 0.197 x + \u03c0/9) where x and y are in cm and t in s. The positive direction of x is from left to right, then what is the value of frequency?\n",
        "input": "frequency = speed/wavelength",
        "output": "13.1 hertz\nThe relationship between angular frequency (\u03c9) and frequency (f) is given by the equation: \u03c9 = 2\u03c0f. Therefore, the frequency (f) can be calculated as: f = \u03c9 / (2\u03c0). In this case, the angular frequency (\u03c9) is \"+str(w)+\" radians/s. Substituting this value into the equation, we can calculate the frequency (f): f = \"+str(w)+\" / (2\u03c0). The calculated value of the frequency will give us the number of complete oscillations of the wave per unit time."
    },
    {
        "instruction": "A short bar magnet of magnetic moment 17.25 J/T is placed in a uniform magnetic field of 9.25 T. If the magnet is free to rotate in the plane of the field, what is the potential energy of the magnet at a position making an angle of 11 degrees with the magnetic field?",
        "input": "-m * b * 0.98",
        "output": "The potential energy of the magnet at a position making an angle of 0.981627183447664 degrees with the magnetic field can be calculated using the formula -m * b * cos(d), where 'm' is the magnetic moment of the bar magnet, 'b' is the magnetic field strength, and 'd' is the angle. Substituting the given values, we have -(17.25) * 9.25 * 0.98 = -1.57e+02 joule."
    },
    {
        "instruction": "Light enters from a material-1 having refractive index 8.7 to material-2 having refractive index 0.6. If the speed of light in material-1 is 48000000 m/s, what is the speed of light in material-2?",
        "input": "Speed of Light in a Material (v) = (n1 * c) / n2",
        "output": "The speed of light in a material can be calculated using the formula v = (n1 * c) / n2, where v is the speed of light in the material, n1 is the refractive index of material-1, c is the speed of light in vacuum, and n2 is the refractive index of material-2., this is the final 696000000.0 m/s"
    },
    {
        "instruction": "A solid cylinder of radius 486 m weighs 2 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 32 m/s. How much work has to be done to stop it?\n",
        "input": "0.5*(0.5+1)*m*v*v",
        "output": "2048.0 joules\n"
    },
    {
        "instruction": "A circular coil of radius 34 cm and 7 turns is rotated about its vertical diameter with an angular speed of 87 rad/s in a uniform horizontal magnetic field of magnitude 1.7 T. Obtain the maximum and average emf induced in the coil. If a coil forms a closed loop of resistance 9 ohm, what is the maximum current in the coil and average power loss due to joule heating?\n",
        "input": "EMF = n * w * b * A, I = EMF / R, P = (EMF * I) / 2",
        "output": "maximum emf: 3.76e+02 volt, average emf: 0 volts, maximum current: 4.18e+01 amp, average power loss: 7.85e+03 joule\n\n\nThe maximum emf induced in the coil can be calculated using the formula EMF = n * w * b * A, where n is the number of turns, w is the angular speed, b is the magnetic field magnitude, and A is the area of the coil.\nThe maximum current in the coil can be calculated using the formula I = EMF / R, where R is the resistance of the coil.\nThe average power loss due to joule heating can be calculated using the formula P = (EMF * I) / 2."
    },
    {
        "instruction": "About 21 percent of the power of a 325 W light bulb is converted to visible radiation. What is the average intensity of the visible radiation at a distance of 20 m from the bulb?\n",
        "input": "Average Intensity = (Percentage Power / Total Power) / (4 * pi * distance^2)",
        "output": "1.29e-03 watt/m2\n\n\nThe average intensity of the visible radiation at a distance 'd' from the bulb can be calculated using the formula Average Intensity = (Percentage Power / Total Power) / (4 * pi * distance^2), where Percentage Power is the percentage of power converted to visible radiation, Total Power is the total power of the light bulb, and 'd' is the distance from the bulb."
    },
    {
        "instruction": "A car weighs 1837 kg. The distance between its front and back axles is 96 m. Its centre of gravity is 88 m behind the front axle. Determine the force exerted by the level ground on each front wheel and each back wheel.",
        "input": "Front Wheel Force = (m * g * (d - x)) / d\nBack Wheel Force = (m * g * x) / d",
        "output": "To calculate the force exerted on the front and back wheels, we use the following formulas:\n\nFront Wheel Force = (m * g * (d - x)) / d\nBack Wheel Force = (m * g * x) / d\n\nWhere,\n- m = Mass of the car\n- g = Acceleration due to gravity\n- d = Distance between front and back axles\n- x = Distance of the car's centre of gravity behind the front axle\n\nSubstituting the given values into the formulas, we find that the force exerted on each front wheel is approximately 1500.2 newtons and the force exerted on each back wheel is approximately 16502.4 newtons."
    },
    {
        "instruction": "A hollow sphere of mass 83 kg rotates about its axis with angular speed 34 rad/s. The radius of the sphere is 34 m. What is the magnitude of angular momentum of the sphere about its axis?",
        "input": "Angular Momentum = c * m * r\u00b2 * w",
        "output": "To calculate the magnitude of the angular momentum, we use the following formula:\n\nAngular Momentum = c * m * r\u00b2 * w\n\nWhere,\n- c = Constant for the object\n- m = Mass of the object\n- r = Radius or length of the object\n- w = Angular speed of the object\n\nThe value of the constant (c) depends on the type of object being considered:\n- For a solid cylinder: c = 1/2\n- For a solid sphere: c = 2/5\n- For a hollow sphere: c = 2/3\n- For a rod: c = 1/3\n\nSubstituting the given values into the formula, we find that the magnitude of the angular momentum is approximately 2174821.3 kg\u00b7m\u00b2."
    },
    {
        "instruction": "A concave mirror produces a real image at a distance of 63 cm from it of a real object placed 378 cm in front of it. What is the magnification of the mirror?",
        "input": "Formula: m = v / u",
        "output": "To find the magnification of the mirror, we use the formula m = v / u, where m is the magnification, v is the distance of the real image, and u is the distance of the real object from the mirror. By substituting the given values into the formula, we can solve for m. In this case, the magnification of the mirror is 0.2., this is the final The magnification of the mirror is 0.2."
    },
    {
        "instruction": "A meter stick of mass 42 g is balanced on a knife edge at its center. When a coin is put at the 41 mark, the stick is found to be balanced at 30 cm. What is the mass of the meter stick?",
        "input": "Mass = (Right Side) / Distance",
        "output": "The mass of the meter stick is approximately 51.3 g.\nRight Side = m * (t - t1) = 42 * (30 - 41)"
    },
    {
        "instruction": "A body is dropped from the top of a building of height 97049 m reaches the ground after 139 s under gravity. With what initial velocity was it dropped?",
        "input": "height (h) = 97049 m, time (t) = 139 s",
        "output": "initial velocity (u) = (height (s) - 0.5 * acceleration (a) * time (t)\u00b2) / time (t)\nu = (97049 - 0.5 * 9.8 * 139\u00b2) / 139\nu = (97049 - 94672.90000000001) / 139\nu = (2376.0999999999913) / 139\nu = 17.1"
    },
    {
        "instruction": "A capacitor with air between it's parallel plates, each plate has an area of 0.1016 m2 and the distance between the plates is 964 mm. Calculate the capacitance of the capacitor?\n",
        "input": "C = (\u03b5\u2080 * A) / d",
        "output": "9.33e-01 pico-farad\n\n\n Explanation: To calculate the capacitance C of a capacitor with air between its parallel plates, we use the formula above. In the formula, \u03b5\u2080 represents the permittivity of free space, A represents the area of each plate, and d represents the distance between the plates. By multiplying the permittivity of free space by the plate area and dividing it by the plate separation, we can determine the capacitance of the capacitor"
    },
    {
        "instruction": "A double convex lens has radii of curvatures 74 cm and 11 cm, and is made of material with a refractive index of 1.06. What is the focal length of the lens?",
        "input": "Formula: f = 1 / ((mu - 1) * ((1 / r1) - (1 / r2)))",
        "output": "To find the focal length of the double convex lens, we use the formula f = 1 / ((mu - 1) * ((1 / r1) - (1 / r2))), where f is the focal length, mu is the refractive index of the lens material, r1 is the radius of curvature of the first surface, and r2 is the radius of curvature of the second surface. By substituting the given values into the formula, we can solve for f. In this case, the focal length of the lens is 159.61 cm., this is the final The focal length of the lens is 159.61 cm."
    },
    {
        "instruction": "A stone tied to the end of a string 119 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 71 revolutions in 29 s, what is the magnitude and direction of acceleration of the stone?",
        "input": "a = v\u00b2/r, v = 2\u03c0r/T",
        "output": "a = 281.6 ms-2, towards the centre of the circle, v = 15.4 rad/s\n {explanation}}"
    },
    {
        "instruction": "Two long and parallel straight wires A and B carrying currents of 22 A and 21 A in the opposite direction are separated by a distance 65 cm. Estimate the force and its nature on the 9 cm section of wire B.",
        "input": "Force = (mu * i1 * i2 * l) / (2 * pi * r)",
        "output": "To calculate the force and its nature, we use the following formula:\n\nForce = (mu * i1 * i2 * l) / (2 * pi * r)\n\nSubstituting the given values:\n- mu = 4 * pi * 10^(-7) TmA^-1\n- i1 = 22 A\n- i2 = 21 A\n- r = 65 cm\n- l = 9 cm\n\nAfter evaluating the formula, we find that the force on the 9 cm section of wire is approximately 1.28e-05 newtons and repulsive."
    },
    {
        "instruction": "Two stars each of one solar mass 86000000000000000000000000000000 kg are approaching each other for a head-on collision. When they are at a distance 8000000000 km, their speeds are negligible. What is the speed with which they collide? The radius of each star is 690000 km. Assume the stars remain undistorted until they collide.",
        "input": "Speed = sqrt((-G*m/R) + (G*m/(2*r))) = sqrt(((-6.67 * 10^-11) * 86000000000000000000000000000000) / (8000000000000)) + ((6.67 * 10^-11) * 86000000000000000000000000000000) / (1380000000))",
        "output": "The speed with which the stars collide is approximately 2.04e+06 m/s."
    },
    {
        "instruction": "A particle starts from origin at t = 0 s with a velocity of (1) i + (5) j ms-1 and moves in x-y plane with a constant acceleration of (-4) i + (-2) j ms-2, then what is the y-coordinate after t = 13 s",
        "input": "s = ut + (1/2) * a * t^2",
        "output": "y-coordinate = -104.0 m"
    },
    {
        "instruction": "Light enters from air to glass. If the speed of light in vacuum is 3 x 10^8 m/s and in glass is 50217000 m/s, what is the refractive index of the glass?",
        "input": "Refractive Index (n) = c / v",
        "output": "The refractive index of a material is defined as the ratio of the speed of light in vacuum to the speed of light in the material. It can be calculated using the formula n = c / v, where n is the refractive index, c is the speed of light in vacuum, and v is the speed of light in the material., this is the final 6.0"
    },
    {
        "instruction": "What is the lowest total resistance that can be secured by combinations of three coils of resistance 120, 34, 23?",
        "input": "R_total = (R1 * R2 * R3) / (R1 * R2 + R2 * R3 + R3 * R1)",
        "output": "The lowest combination of resistances can be obtained by connecting them in parallel. The total resistance is calculated as (120 * 34 * 23) / (120 * 34 + 34 * 23 + 23 * 120) = 12.3 ohm.\n\nTo calculate the lowest combination of resistances, we connect them in parallel. The total resistance (R_total) is given by the formula (R1 * R2 * R3) / (R1 * R2 + R2 * R3 + R3 * R1), where R1, R2, and R3 are the individual resistances."
    },
    {
        "instruction": "A steel wire has a length of 28 m and a mass of 229 kg. What should be the tension in the wire so that speed of a transverse wave on the wire equals the speed of sound in dry air at 18 degree C = 340 ms-1.\n",
        "input": "Speed^2 = Tension*length/mass",
        "output": "9.45e+05 newton\nTo determine the time it takes for a disturbance to travel from one end of a string to the other, we can use the wave speed equation for transverse waves on a string. The wave speed (v) on a string is given by: v = sqrt(T / \u03bc), where T is the tension in the string and \u03bc is the linear mass density of the string, which is given by the mass per unit length (\u03bc = m / l)."
    },
    {
        "instruction": "Find the focal length of a convex mirror whose radius of curvature is 5348.26 cm.",
        "input": "Formula: f = R/2",
        "output": "To find the focal length of a convex mirror, we use the formula f = R/2, where f is the focal length and R is the radius of curvature. By substituting the given value of R into the formula, we can solve for f. In this case, the focal length is 2674.1 cm., this is the final 2674.1"
    },
    {
        "instruction": "Suppose we employ a system of units in which the unit of mass equals 56 kg, the unit of length equals 41 m, the unit of time is 24 s, if the value of x newton is equal to 6 units in new system, find x?\n",
        "input": "x N = (m kg) * (l m) / (t^2 s^2)",
        "output": "23.92\nTo find the value of x newtons in the given system of units, we need to consider the relationships between the units of mass (kg), length (m), time (s), and force (Newton). In the new system of units, we have: 1 unit of mass = 23.92\n kg, 1 unit of length = 41 m, 1 unit of time = 24 s. To find the value of x newtons, we need to determine the conversion factors between the new system and the standard SI units. The force (Newton) can be expressed as: x N = (m kg) * (l m) / (t^2 s^2). Substituting the given values into this equation, we have: x N = (m * 23.92\n kg) * (l * 41 m) / (t^2 * 24 s^2). Simplifying this expression will give us the value of x in newtons."
    },
    {
        "instruction": "A girl sitting on a merry-go-round is moving in a counter-clockwise arc length of 434 m. If the angular displacement is 298 rad, how far is she from the center of the merry-go-round?",
        "input": "distance_from_center = arc_length / radius",
        "output": "To calculate the distance from the center, we use the following formula:\n\ndistance_from_center = arc_length / radius\n\nSubstituting the given values into the formula, we find that the distance from the center is approximately 1.5 m."
    },
    {
        "instruction": "A force of 159 +/- 8 N is applied over an area of 2.91 +/- 0.03 m2. Calculate the pressure exerted over the area.\n",
        "input": "Pressure = Force/Area",
        "output": "54.64+/-3.31\nTo calculate the pressure exerted over an area, we use the formula: Pressure = Force / Area. In this case, the force applied is 159 N, and the area is 2.91 m\u00b2. The error in the force measurement is 8 N, and the error in the area measurement is 0.03 m\u00b2. To determine the error in the pressure calculation, we can use error propagation. The formula for calculating the maximum error in a function involving measured quantities is: Max Error = |dP/dx| * \u0394x, where Max Error is the maximum error, dP/dx is the derivative of the function with respect to the measured quantity (force or area), and \u0394x is the error in the measured quantity. Taking the derivative of the pressure formula with respect to force and area, we have: dP/dF = 1 / A, dP/dA = -F / A\u00b2. Substituting the given values into the error propagation formula, we can calculate the maximum error in the pressure: Max Error = |(1 / A_val) * F_error| + |(-F_val / A_val\u00b2) * A_error|. Now, we can substitute the given values to calculate the pressure and its maximum error over the given area."
    },
    {
        "instruction": "Four point charges q1 = -1 x 10^(-6) C, q2 = 12 x 10^(-6) C, q3 = 18 x 10^(-6) C, q4 = 4 x 10^(-6) C, are located at corners of square ABCD of side 15 cm. What is the force on a charge of 8 x 10^(-6) C placed at the centre of the square?\n",
        "input": "Force (F) = k * |q1 - q3| * |q2 - q4| * q_c / (d^2)",
        "output": "To calculate the force on the charge placed at the center of the square, we use the formula for electric force between two point charges:\nForce (F) = k * |q1 - q3| * |q2 - q4| * q_c / (d^2)\nwhere k is Coulomb's constant (9 * 10^9 N\u00b7m\u00b2/C\u00b2), q1, q2, q3, q4 are the charges at the corners of the square (in Coulombs), q_c is the charge placed at the center of the square (in Coulombs), and d is the side length of the square (in meters).\nGiven q1 = -1 x 10^(-6) C, q2 = 12 x 10^(-6) C, q3 = 18 x 10^(-6) C, q4 = 4 x 10^(-6) C, d = 15 cm, and q_c = 8 x 10^(-6) C:\nForce (F) = 6.60e+01 N\n"
    },
    {
        "instruction": "What is the energy associated with a mass of 34.5 g ?\n",
        "input": "Energy = Mass*c^2",
        "output": "3.10e+15joule\nTo calculate the energy associated with a mass, we need to specify the type of energy we are referring to. There are various forms of energy, such as kinetic energy, potential energy, thermal energy, etc. If we assume you are referring to the energy associated with the mass in terms of its rest energy, we can use Einstein's mass-energy equivalence principle, given by the equation: E = m * c^2"
    },
    {
        "instruction": "In a p-n junction diode, the current I can be expressed as I = I0*exp((e*V/2*k_b*T)-1), k_b = 8.6 * 10^(-5) eV/K. If for given diode I0 = 1436 x 10^(-15) A and T = 284 K, what will be dynamic resistance if the voltage across the diode is increased from 1.0 V to 2.8 V?\n",
        "input": "I=Io*exp((e*V/2*Kb*T)-1), R = V2/I2-I1",
        "output": "5.55e-38 ohm\nCalculate the resistance by dividing the increased voltage and the increase in current"
    },
    {
        "instruction": "Two spheres q1 of charge 53 x 10^(-6)C, q2 of charge -136 x 10^(-6)C are placed at a distance 111 cm. If an uncharged sphere C first comes in contact with A, then with B and placed at 111 cm from both of them, then what is the final charge on A?\n",
        "input": "Final charge on A = qa / 2",
        "output": "The final charge on sphere A can be calculated by dividing the initial charge qa by 2. Therefore, the final charge on A is 26.5 coulomb\n"
    },
    {
        "instruction": "What is the kinetic energy of an object of mass 756 kg moving with a velocity of 647 m/s?",
        "input": "KE = 1/2 * m * v^2",
        "output": "To calculate the kinetic energy, we use the formula KE = 1/2 * m * v^2, where KE is the kinetic energy, m is the mass (756 kg), and v is the velocity (647 m/s)., this is the final answer 158234202.0"
    },
    {
        "instruction": "Let us assume that our galaxy consists of 58 * 10^9 stars each of one solar mass. How long will a star at a distance of 69281 ly from the galactic centre take to complete one revolution? Take the diameter of the Milky Way to be 10^5 ly.",
        "input": "No. of Stars = 58 * 10^9, Distance = 69281 ly",
        "output": "2.793e-05 s"
    },
    {
        "instruction": "A parallel plate capacitor made of circular plates of radius r = 107 cm has a capacitance C = 4 pF. The capacitor is connected to a 230 V ac supply with an angular frequency of 900 rad/s. What is the rms value of the conduction current?",
        "input": "I = 8.28e-07 ampere",
        "output": "8.28e-07 ampere\n\nThe rms value of the conduction current can be calculated by taking the square root of the average of the square of the current."
    },
    {
        "instruction": "A compound microscope has a magnification of 139. The focal length of the eyepiece is 14 cm. Assuming that the final image is formed at a least distance of distinct vision (25 cm), find the magnification produced by the objective.",
        "input": "Formula: M_objective = M_eyepiece * (1 + (d / f_eyepiece))",
        "output": "To find the magnification produced by the objective, we can use the formula M_objective = M_eyepiece * (1 + (d / f_eyepiece)), where M_objective is the magnification produced by the objective, M_eyepiece is the magnification of the eyepiece, d is the least distance of distinct vision (25 cm), and f_eyepiece is the focal length of the eyepiece. By substituting the given values into the formula, we find that the magnification produced by the objective is 387.2142857142857X., this is the final 3.87e+02X"
    },
    {
        "instruction": "If a monoatomic gas of 1 moles at 55 atm and volume 155 lit is adiabatically changed to volume 122 lit, then what will be the pressure.\n",
        "input": "P1*(V1^1.66)=P2*(V2^1.66)",
        "output": "81.8atm\nTo calculate the final pressure of the monoatomic gas after an adiabatic expansion, we can use the adiabatic equation: P1 * V1^\u03b3 = P2 * V2^\u03b3, where P1 and V1 are the initial pressure and volume, P2 and V2 are the final pressure and volume, and \u03b3 is the heat capacity ratio. The heat capacity ratio (\u03b3) for a monoatomic gas is typically 5/3."
    },
    {
        "instruction": "In a chamber, a uniform magnetic field of 0.0002 T is maintained. An electron is shot into the field with a speed of 71000000 m/s, making an angle of 53 degrees with the field. Determine the frequency of the revolution of the electron.",
        "input": "Frequency of revolution = (b * e) / (2 * pi * m)",
        "output": "To calculate the frequency of revolution, we use the following formula:\n\nFrequency of revolution = (b * e) / (2 * pi * m)\n\nSubstituting the given values:\n- b = 0.0002 T\n- e = 1.6000000000000002e-19 C\n- m = 9.1e-31 kg\n\nAfter evaluating the formula, we find that the frequency of revolution is approximately 5.60e+06 sec^-1."
    },
    {
        "instruction": "Two strips of metal are riveted together at their ends by four rivets, each of diameter 5 mm. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed 13905400?",
        "input": "",
        "output": "The maximum tension that can be exerted by the riveted strip is 1.1e+03 newton."
    },
    {
        "instruction": "In a circuit with a battery of potential difference 930 V, if the rate of heat generated is 776 W, calculate the current in the circuit?",
        "input": "I = P / V",
        "output": "0.8 ampere\n\nThe current in the circuit can be calculated using the formula: I = P / V, where P is the rate of heat generated and V is the potential difference."
    },
    {
        "instruction": "A bullet fired at an angle of 55 degrees with the horizontal hits the ground 267 m away. By adjusting its angle of projection, can one hope to hit a target 442 m away?",
        "input": "no",
        "output": "The target is too far away to be hit."
    },
    {
        "instruction": "A bat is flitting about in a cave, navigating via ultrasonic beeps. Assume that the sound emission frequency of the bat is 39450 Hz. During one fast swoop directly toward a flat wall surface, the bat is moving at 0.0317 times the speed of sound in air. What frequency does the bat hear reflected off the wall?\n",
        "input": "apparent frequency = [{(speed of air + speed of bat)}/speed of air]*apparent frequency of sound striking the wall",
        "output": "4.20e+04 hertz\nThe concept of Doppler's effect has been applied to calculate apparent frequencies."
    },
    {
        "instruction": "A tank is filled with water to a height of 175.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 127.0 cm. What is the refractive index of water?",
        "input": "Formula: refractive index = height of tank / apparent depth of needle",
        "output": "To calculate the refractive index, we use the formula: refractive index = height of tank / apparent depth of needle. In this case, the height of the tank is 175.5 cm and the apparent depth of the needle is 127.0 cm., this is the final 1.38"
    },
    {
        "instruction": "A convex mirror produces a real image of height 3 cm at a distance of 1 cm from it of a real object having a height of 12 cm. At what distance is the object placed from the mirror?",
        "input": "Formula: m = v / u = hi / ho",
        "output": "To find the distance of the object from the mirror, we use the formula m = v / u = hi / ho, where m is the magnification, v is the distance of the image from the mirror, u is the distance of the object from the mirror, hi is the height of the image, and ho is the height of the object. By rearranging the formula, we can calculate u as u = (ho * v) / hi. By substituting the given values into the formula, we find that the object is placed at a distance of 4.0 cm from the mirror., this is the final The object is placed at a distance of 4.0 cm from the mirror."
    },
    {
        "instruction": "A police van moving on a highway with a speed of 225 m/s fires a bullet at a thief's car speeding away in the same direction with a speed of 395 m/s. If the muzzle speed of the bullet is 1083 m/s, with what speed does the bullet hit the thief's car?",
        "input": "v1 = 225 m/s, v2 = 395 m/s, v3 = 1083 m/s",
        "output": "The speed of the bullet is 1308 m/s, and the relative speed of the bullet with respect to the thief's car is 913 m/s"
    },
    {
        "instruction": "A hollow sphere and a solid cylinder roll down two different inclined planes of heights 13 and 1 and with angles of inclination of 38 and 79, which one reaches the bottom with more speed?",
        "input": "speed = height / (1 + k)",
        "output": "To compare the speeds, we use the following formula:\n\nspeed = height / (1 + k)\n\nSubstituting the given values into the formula, we find that:\n\nThe hollow sphere reaches the bottom with more speed."
    },
    {
        "instruction": "A 2 cm of wire carrying a current of 37 A is placed inside a solenoid making an angle of 57 degrees with its axis. The magnetic field inside the solenoid is 71 tesla. Find the magnetic force on the wire.",
        "input": "Force per unit length = b * i * sin(d)",
        "output": "To calculate the magnitude of the magnetic force, we use the following formula:\n\nForce per unit length = b * i * sin(d)\n\nSubstituting the given values:\n- b = 71 tesla\n- i = 37 A\n- d = 57 degrees\n\nAfter evaluating the formula, we find that the magnetic force per unit length is approximately 44.064 newtons."
    },
    {
        "instruction": "An object is placed at 792 cm in front of a convex lens. Image is formed at a distance of 259 cm behind it. Find the focal length of the lens.",
        "input": "Formula: 1/f = 1/v - 1/u for convex lens.",
        "output": "To find the focal length of the lens, we use the formula for convex lenses: 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for f. In this case, the focal length of the lens is 195.2 cm., this is the final The focal length of the lens is 195.2 cm."
    },
    {
        "instruction": "A circular disc, of mass 18080 g, is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. If the period of torsional oscillations is 1900 ms, and the radius of the disc is 29 cm, determine the torsional spring constant of the wire.",
        "input": "Formula: alpha = (2\u03c0^2 * (m / 1000) * (r / 100)^2) / (t / 1000)^2, where alpha is the torsional spring constant, m is the mass of the disc in grams (18080 g), r is the radius of the disc in centimeters (29 cm), and t is the period of torsional oscillations in milliseconds (1900 ms).",
        "output": "Using this formula: Formula: alpha = (2\u03c0^2 * (m / 1000) * (r / 100)^2) / (t / 1000)^2, where alpha is the torsional spring constant, m is the mass of the disc in grams (18080 g), r is the radius of the disc in centimeters (29 cm), and t is the period of torsional oscillations in milliseconds (1900 ms)., this is the final answer derived: 8.31e+00 newton-m rad-1"
    },
    {
        "instruction": "Earthquakes generate sound waves inside the earth, assuming the speed of transverse(S) wave is 3450 ms-1, speed of longitudinal(P) wave is 3970 ms-1, if the first P wave arrives 396 s before the first S wave to seismograph, at what distance does the earthquake occur?\n",
        "input": "Vs*Ts=Vp*Tp, L = Vp*Tp",
        "output": "1.04e+04 km\nTo determine the distance to the earthquake epicenter, we can use the difference in arrival times between the P wave and S wave at the seismograph.Using the formula for distance (d) based on wave speed and time: d = (P wave speed - S wave speed) * t"
    },
    {
        "instruction": "At temperature (171 degree C) the resistance of a heating element is 367 ohm. What is the temperature of the element if the resistance is found to be 387 ohm (temp coeff = 1.7 x 10^(-4) degree C-1)?",
        "input": "T = ((R2 - R1) / (R1 * temp_coeff)) + T1",
        "output": "491.6 degree centigrade\n\nTo calculate the temperature of the element, use the formula: T = ((R2 - R1) / (R1 * temp_coeff)) + T1, where R2 is the final resistance, R1 is the initial resistance, temp_coeff is the temperature coefficient, and T1 is the initial temperature."
    },
    {
        "instruction": "A concave mirror produces a virtual image of height 951 cm of a real object of height 928 cm placed in front of it. What is the magnification of the mirror?",
        "input": "Formula: m = hi / ho",
        "output": "To find the magnification of the mirror, we use the formula m = hi / ho, where m is the magnification, hi is the height of the virtual image, and ho is the height of the real object. By substituting the given values into the formula, we can solve for m. In this case, the magnification of the mirror is 1.0., this is the final The magnification of the mirror is 1.0."
    },
    {
        "instruction": "A double concave lens has radii of curvatures 76 cm and 64 cm, and is made of material with a refractive index of 1.23. What is the focal length of the lens?",
        "input": "Formula: f = 1 / ((mu - 1) * ((1 / r1) - (1 / r2)))",
        "output": "To find the focal length of the double concave lens, we use the formula f = 1 / ((mu - 1) * ((1 / r1) - (1 / r2))), where f is the focal length, mu is the refractive index of the lens material, r1 is the radius of curvature of the first surface, and r2 is the radius of curvature of the second surface. By substituting the given values into the formula, we can solve for f. In this case, the focal length of the lens is -151.06 cm., this is the final The focal length of the lens is -151.06 cm."
    },
    {
        "instruction": "An object is projected at an angle 61 from the ground, if the horizontal range of the object is 10339 m, what is the initial velocity of it?",
        "input": "h = 10339 m, theta = 61 degrees",
        "output": "345.7"
    },
    {
        "instruction": "A prism is made of glass of unknown refractive index. A parallel beam of light is incident on a face of the prism. The angle of minimum deviation is measured to be 51\u00b0. What is the refractive index of the material of the prism? The refracting angle of the prism is 19\u00b0. If the prism is placed in liquid (refractive index 2.08), predict the new angle of minimum deviation of a parallel beam of light.",
        "input": "Refractive Index (\u03bc) = sin\u2061((A+D)/2) / sin\u2061(D/2), Angle of Minimum Deviation (\u03b4m) = 2 * (sin\u2061((A+D)/2) / sin\u2061(D/2)), New Angle of Minimum Deviation (\u03b4m') = 2 * (sin\u2061(D/2) * (\u03b4m / \u03bc) - D/2)",
        "output": "The refractive index of a material is defined as the ratio of the speed of light in vacuum to the speed of light in the material. The angle of minimum deviation (\u03b4m) of a prism is the angle between the incident ray and the emergent ray that produces the minimum deviation. It can be calculated using the formula \u03b4m = 2 * (sin\u2061((A+D)/2) / sin\u2061(D/2)), where A is the angle of incidence and D is the angle of deviation. When the prism is placed in a medium with a different refractive index, the new angle of minimum deviation (\u03b4m') can be predicted using the formula \u03b4m' = 2 * (sin\u2061(D/2) * (\u03b4m / \u03bc) - D/2), where \u03bc is the refractive index of the medium., this is the final The refractive index of the material of the prism is 3.48e+00 and the new angle of minimum deviation is 1.30e+01\u00b0."
    },
    {
        "instruction": "A batsman deflects a ball by an angle of 180 degrees without changing its initial speed, which is equal to 145 m/s. What is the impulse imparted to the ball? (The mass of the ball is 252 g)",
        "input": "Impulse calculation",
        "output": "-73.1\nThe impulse imparted to the ball can be calculated using the formula (2 * mass * velocity * cos(angle)) / 1000, where the mass is 252 g, the velocity is 145 m/s, and the angle is 180 degrees. The result is -73.1 kg\u00b7m/s, perpendicular to the point of impact on the bat."
    },
    {
        "instruction": "A long straight wire in the horizontal plane carries a current of of 479 A in west to east direction. What is the magnitude and direction of the magnetic field B at a point 870 cm south of the wire.\n",
        "input": "B = (mu * i) / (2 * pi * r)",
        "output": "To calculate the magnitude and direction of the magnetic field B, we use the following formula:\n\nB = (mu * i) / (2 * pi * r)\n\nWhere,\n- B = Magnetic field\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- i = Current flowing through the wire\n- r = Distance from the wire\n\nSubstituting the given values into the formula, we find that the magnitude and direction of the magnetic field B is approximately 1.1e-05 tesla vertically downwards\n."
    },
    {
        "instruction": "A convex lens produces a virtual image at a distance of 916 cm from it of a real object placed 539 cm in front of it. What is the magnification of the lens?",
        "input": "Formula: m = v / u",
        "output": "To calculate the magnification of the lens, we use the formula m = v / u, where m is the magnification, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for m. In this case, the magnification of the lens is 1.7., this is the final The magnification of the lens is 1.7."
    },
    {
        "instruction": "A wheel, when applied with a constant angular acceleration of 100 rad/s\u00b2, reaches a velocity of 17258 rad/s when the angular position is 86 rad. What is its initial angular velocity?",
        "input": "initial_angular_velocity = sqrt(final_angular_velocity^2 - (2 * angular_acceleration * angular_position))",
        "output": "To calculate the initial angular velocity, we use the following formula:\n\ninitial_angular_velocity = sqrt(final_angular_velocity^2 - (2 * angular_acceleration * angular_position))\n\nSubstituting the given values into the formula, we find that the initial angular velocity is approximately 17257.5 rad/s."
    },
    {
        "instruction": "A tank is filled with a liquid of refractive index 203 to a height of 161.8 cm. What is the apparent depth of a needle lying at the bottom of the tank?",
        "input": "Formula: apparent depth of needle = height of tank / refractive index",
        "output": "To calculate the apparent depth of the needle, we use the formula: apparent depth of needle = height of tank / refractive index. In this case, the height of the tank is 161.8 cm and the refractive index is 203., this is the final 0.8 cm"
    },
    {
        "instruction": "A body is dropped with an initial velocity of 940 m/s and reaches the ground with a velocity of 1134 m/s. From what height was it dropped?",
        "input": "initial velocity (u) = 940 m/s, final velocity (v) = 1134 m/s",
        "output": "height (h) = (final velocity (v)\u00b2 - initial velocity (u)\u00b2) / (2 * acceleration (g))\nh = (1134\u00b2 - 940\u00b2) / (2 * 9.8)\nh = (1285956 - 883600) / 19.6\nh = 20528.4"
    },
    {
        "instruction": "An object of mass 2532 g stands on a weighing machine in a lift, which is moving upwards with a uniform speed of 980 cm/s.",
        "input": "Scale Reading = m * 10 - v",
        "output": "24340\nTo calculate the scale reading, we use the formula Scale Reading = mass * 10 - velocity, where the mass is 2532 g and the velocity is 980 cm/s."
    },
    {
        "instruction": "A girl sitting on a merry-go-round is moving in a counter-clockwise arc length of 723 m. If the angular displacement is 643 rad, how far is she from the center of the merry-go-round?",
        "input": "distance_from_center = arc_length / radius",
        "output": "To calculate the distance from the center, we use the following formula:\n\ndistance_from_center = arc_length / radius\n\nSubstituting the given values into the formula, we find that the distance from the center is approximately 1.1 m."
    },
    {
        "instruction": "A copper wire has a cross-sectional area of 98 m\u00b2 and length of 72 m. What is the resistivity of this wire that makes its resistance 45 ohm?",
        "input": "R = 45 ohm, A = 98 m\u00b2, l = 72 m",
        "output": "The resistivity of the wire required to achieve a resistance of 45 ohm is 61.2 ohm-m. It is calculated by dividing the product of resistance and area (4410) by the length."
    },
    {
        "instruction": "A piece of copper having a rectangular cross-section of 92 mm x 6 mm is pulled in tension with 6800 N force, producing only elastic deformation. Calculate the resulting strain? Shear modulus of elasticity of copper is 42 x 10^9 N/m^2.",
        "input": "strain = force / (A * (shear_modulus * 10^9))",
        "output": "To calculate the resulting strain, we use the formula:\n\nstrain = force / (A * (shear_modulus * 10^9))\n   = 6800 N / (92 mm * 6 mm * 10^-6 m^2 * (42 * 10^9 N/m^2))\n   = 293.3 x 10^(-6)."
    },
    {
        "instruction": "A radio can tune over the frequency range of a portion of MW broadcast band: (206 kHz to 435 kHz). If its LC circuit has an effective inductance of 324 muH, what must be the range of its variable capacitor?",
        "input": "w1 = 2 * pi * f1\nC1 = 1 / ((w1 ** 2) * L)\nw2 = 2 * pi * (f1 + f2)\nC2 = 1 / ((w2 ** 2) * L)",
        "output": "4.13e-10 farad to 1.84e-09 farad"
    },
    {
        "instruction": "A bike starting with an initial velocity of 949 m/s travels on a straight road at a constant rate of 87 m/s\u00b2 for 7 s. How far does the bike travel during this time?",
        "input": "initial velocity (u) = 949 m/s, acceleration (a) = 87 m/s\u00b2, time (t) = 7 s",
        "output": "8774.5 m \n\ndistance (s) = initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)\u00b2\ns = 949 * 7 + 0.5 * 87 * 7\u00b2\ns = 6643 + 2131.5\ns = 8774.5"
    },
    {
        "instruction": "Calculate the charge (in C) of 2.10e+18 electrons?",
        "input": "Q = n * e",
        "output": "3.00e-01 coulomb\n\nThe charge of electrons can be calculated using the formula: Q = n * e, where n is the number of electrons and e is the charge of an electron."
    },
    {
        "instruction": "A point charge of 2.483e-06 C is at the center of a cubic Gaussian surface with an edge length of 211 cm. What is the net flux through the surface?\n",
        "input": "Net flux = (Q / epsilon_0)",
        "output": "To calculate the net flux through the surface, we use the formula:\nNet flux = (Q / epsilon_0)\nGiven charge Q = 2.483e-06 C,\nNet flux = 2.80e-04 N\u00b7m\u00b2/C\n"
    },
    {
        "instruction": "An LC circuit contains a 108 mH inductor and a 145 muF capacitor with an initial charge of 23 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0. At what time(s) energy stored in electrical form is 31 percent of total energy?",
        "input": "Time = n * T, where n is an integer\nT = 1 / (Natural Frequency)",
        "output": "0.16t, 0.66t, 1.16t, ...; where t = 2.49e-02 s"
    },
    {
        "instruction": "Two bodies A, B of masses 40 kg and 4 kg respectively kept on a smooth, horizontal surface are tied to the ends of a tight string. A horizontal force F = 88 N is applied to B along the direction of the string. What is the acceleration and tension in the string?",
        "input": "",
        "output": "The acceleration is 2.0 m/s^2, and the tension is 80.0 N."
    },
    {
        "instruction": "A truck starts from rest and accelerates uniformly at 18 ms-2. At t = 78 s, a stone is dropped by a person standing on the top of the truck (4 m high from the ground). What are the (a) velocity, and (b) acceleration of the stone at t = 89 s? (Neglect air resistance.)",
        "input": "A truck starts from rest and accelerates uniformly at 18 ms-2. At t = 78 s, a stone is dropped by a person standing on the top of the truck (4 m high from the ground). What are the (a) velocity, and (b) acceleration of the stone at t = 89 s? (Neglect air resistance.)",
        "output": "Velocity is 1408.3 ms-1, at an angle of 4 degrees with horizontal. Acceleration is g (10 ms-2) downwards."
    },
    {
        "instruction": "A stone tied to the end of a string 177 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 198 revolutions in 195 s, what is the magnitude and direction of acceleration of the stone?",
        "input": "a = v\u00b2/r, v = 2\u03c0r/T",
        "output": "a = 72.0 ms-2, towards the centre of the circle, v = 6.4 rad/s\n {explanation}}"
    },
    {
        "instruction": "The storage battery of a car has an emf of 1076 V, if the internal resistance of the battery is 998 milliohm, what is the maximum current that can be drawn from the battery?\n",
        "input": "Maximum current = (emf * 1000) / resistance",
        "output": "1078.2\n\nExplanation: The maximum current that can be drawn from a battery can be calculated using Ohm's Law: current = emf / resistance. Here, emf is the electromotive force or voltage of the battery and resistance is its internal resistance. "
    },
    {
        "instruction": "A convex lens produces a real image of height 77 cm of a real object having a height of 85 cm and placed 48 cm in front of it. At what distance is the image formed from the lens?",
        "input": "Formula: v = (u * hi) / ho",
        "output": "To find the distance at which the image is formed from the lens, we use the formula v = (u * hi) / ho, where v is the distance of the image from the lens, u is the distance of the object from the lens, hi is the height of the image, and ho is the height of the object. By substituting the given values into the formula, we can calculate v. In this case, the image is formed at a distance of 43.5 cm from the lens., this is the final The image is formed at a distance of 43.5 cm from the lens."
    },
    {
        "instruction": "What is the electric field at a point P at a distance of 200 m from the center of the spherical shell of radius 282 m and having 1.48e-06 C charge distributed uniformly on it?",
        "input": "Electric Field (E) = 0 N/C",
        "output": "0 newton/coulomb\nFor a spherical shell, the electric field inside the shell is zero."
    },
    {
        "instruction": "A circular disc, of mass 15830 g, is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. If the period of torsional oscillations is 1170 ms, and the radius of the disc is 24 cm, determine the torsional spring constant of the wire.",
        "input": "Formula: alpha = (2\u03c0^2 * (m / 1000) * (r / 100)^2) / (t / 1000)^2, where alpha is the torsional spring constant, m is the mass of the disc in grams (15830 g), r is the radius of the disc in centimeters (24 cm), and t is the period of torsional oscillations in milliseconds (1170 ms).",
        "output": "Using this formula: Formula: alpha = (2\u03c0^2 * (m / 1000) * (r / 100)^2) / (t / 1000)^2, where alpha is the torsional spring constant, m is the mass of the disc in grams (15830 g), r is the radius of the disc in centimeters (24 cm), and t is the period of torsional oscillations in milliseconds (1170 ms)., this is the final answer derived: 1.31e+01 newton-m rad-1"
    },
    {
        "instruction": "A capacitor with air between it's parallel plates, each plate has an area of 0.1063 m2 and the distance between the plates is 1016 mm. Calculate the capacitance of the capacitor?\n",
        "input": "C = (\u03b5\u2080 * A) / d",
        "output": "9.26e-01 pico-farad\n\n\n Explanation: To calculate the capacitance C of a capacitor with air between its parallel plates, we use the formula above. In the formula, \u03b5\u2080 represents the permittivity of free space, A represents the area of each plate, and d represents the distance between the plates. By multiplying the permittivity of free space by the plate area and dividing it by the plate separation, we can determine the capacitance of the capacitor"
    },
    {
        "instruction": "For the travelling harmonic wave y(x, t) = 4 cos 2\u03c0 (7t \u2013 0.027x + 0.35) where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of 15 m?\n",
        "input": "Phase difference = (2pi/wavelength)* Path difference",
        "output": "81.0 \u03c0 rad\nTo calculate the phase difference between two points in a traveling harmonic wave, we need to compare the phase angles of the wave at those points.In the given wave equation, the phase angle is represented by the term inside the cosine function, i.e., 2\u03c0(wt - kx + 0.35), where w represents the angular frequency and k represents the wave number.Let's assume the two points are at x1 and x2, separated by a distance \u0394x = x2 - x1. The phase difference between the oscillatory motion of these two points can be calculated using the equation: Phase difference = 2\u03c0(k\u0394x)"
    },
    {
        "instruction": "A small bulb is placed at the bottom of a tank containing liquid to a depth of 32 cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of the liquid is 1.26.",
        "input": "Formula: Area = \u03c0 * h\u00b2 * (k / (1 - k)), where h is the depth of the liquid in centimeters, and k is the reciprocal of the refractive index of the liquid.",
        "output": "This is the answer 0.55 m\u00b2, formula used is : Formula: Area = \u03c0 * h\u00b2 * (k / (1 - k)), where h is the depth of the liquid in centimeters, and k is the reciprocal of the refractive index of the liquid."
    },
    {
        "instruction": "The edge of a cube is 42 cm long. One face of the cube is firmly fixed to a vertical wall. A mass of 86 kg is then attached to the opposite face of the cube. The shear modulus of the material of the cube is 188 GPa. What is the vertical deflection of this face?",
        "input": "deflection = (mass * 9.8) / (Y * 10^9 * (edge_length * 10^-2))",
        "output": "To calculate the vertical deflection, we use the formula:\n\ndeflection = (mass * 9.8) / (Y * 10^9 * (edge_length * 10^-2))\n   = (86 kg * 9.8) / (188 * 10^9 GPa * (42 cm * 10^-2 m/cm))\n   = 10.7 nm."
    },
    {
        "instruction": "What is the gravitational field at a point P at a distance of 455 m from the center of the uniform solid sphere of radius 463 m and mass 100 kg?",
        "input": "Gravitational Field (g) = cal2(100, 455, 463) N/kg",
        "output": "The gravitational field at a point P at a distance of 455 m from the center of the uniform solid sphere of radius 463 m and mass 100 kg is given by the formula g = (-G * m * r) / (R^3), where G is the gravitational constant, m is the mass, r is the distance, and R is the radius. Plugging in the values, we get g = -3.06e-14 N/kg."
    },
    {
        "instruction": "If a wheel of radius 403 m has an angular acceleration of 238 rad/s\u00b2, what is the acceleration of a point at the circumference of the wheel?",
        "input": "acceleration_at_circumference = angular_acceleration * radius",
        "output": "To calculate the acceleration at the circumference, we use the following formula:\n\nacceleration_at_circumference = angular_acceleration * radius\n\nSubstituting the given values into the formula, we find that the acceleration at the circumference is approximately 95914 m/s\u00b2."
    },
    {
        "instruction": "A convex mirror produces 23 times diminished real image of an object at a distance of 62 cm from the mirror. At what distance is the object placed in front of the mirror?",
        "input": "Formula: u = v * n",
        "output": "To find the distance at which the object is placed in front of the mirror, we use the formula u = v * n, where u is the distance of the object from the mirror, v is the distance of the image from the mirror, and n is the magnification factor. By substituting the given values into the formula, we can calculate u. In this case, the object is placed at a distance of 1426 cm in front of the mirror., this is the final The object is placed at a distance of 1426 cm in front of the mirror."
    },
    {
        "instruction": "An object is placed at 294 cm in front of a concave lens of focal length 640 cm. Find at what distance image is formed and its nature.",
        "input": "Formula: 1/f = 1/v - 1/u for concave lens.",
        "output": "This is the answer The image is formed at 201 cm and it is virtual., formula used is : Formula: 1/f = 1/v - 1/u for concave lens."
    },
    {
        "instruction": "A capacitor with air between its parallel plates, each plate has an area of 0.0868 m\u00b2 and the distance between the plates is 26 mm. If this capacitor is connected to a 442 V supply and a 26 mm thick mica sheet is inserted between the plates, then what will happen?",
        "input": "A = 0.0868 m\u00b2, d = 26 mm, V = 442 V",
        "output": "capacitance becomes = 6 * 2.96e+01 = 1.77e+02 pico-farad, charge = capacitance * V = 1.77e-10 * 442 = 7.84e-08 coulomb\n\nWhen the mica sheet is inserted between the plates, the effective capacitance of the capacitor changes, and the charge on the capacitor can be calculated using the formula Q = CV."
    },
    {
        "instruction": "An infinite line charge produces a field of 7305 N/C at a distance of 166 cm. Calculate the linear charge density.\n",
        "input": "Linear charge density = (Electric field * distance) / (18 * epsilon_0)",
        "output": "To calculate the linear charge density, we use the formula:\nLinear charge density = (Electric field * distance) / (18 * epsilon_0)\nGiven electric field = 7305 N/C, distance = 166 cm,\nLinear charge density = 6.74e-07 C/m\n"
    },
    {
        "instruction": "What is the density of water at a depth where pressure is 189800 Pa, given that its density at the surface is 1006 kg/m^3?",
        "input": "density = surface_density / (1 - depth * 45.8 * 10^(-8))",
        "output": "The density of water at a depth of 189800 Pa is approximately 1101.8 kg/m^3. To calculate the density, we use the formula:\n\ndensity = surface_density / (1 - depth * 45.8 * 10^(-8))"
    },
    {
        "instruction": "From a rifle of mass 9700 g, a bullet of mass 21 g is fired with a velocity of 950 m/s, then calculate the recoil velocity of the rifle (in m/s)?",
        "input": "Calculate recoil velocity, rifle mass, bullet velocity, or bullet mass",
        "output": "2.1 m/s"
    },
    {
        "instruction": "An object is placed at 1341 cm in front of a convex lens of focal length 250 cm. Find at what distance image is formed and its nature.",
        "input": "Formula: 1/f = 1/v - 1/u for convex lens.",
        "output": "To find the distance of the image formed, we use the formula for convex lenses: 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for v. In this case, the image is real and located at a distance of 307.3 cm., this is the final The image is formed at 307.3 cm and it is real."
    },
    {
        "instruction": "A plane electromagnetic wave travels in vacuum along the z-direction. If the frequency of the wave is 73123800 Hz, what is its wavelength?",
        "input": "f = 73123800 Hz",
        "output": "4.10e+00 m\n\nThe wavelength of the wave can be calculated by dividing the speed of light by the frequency."
    },
    {
        "instruction": "If a diatomic gas of 2 moles at 191 atm and volume 127 lit is isothermally changed to pressure 197 atm, then what will be its volume.\n",
        "input": "P1*V1 = P2*V2",
        "output": "123.1lit\nTo determine the final volume of a diatomic gas after an isothermal expansion, we can use Boyle's Law, which states that for an ideal gas at constant temperature: P1 * V1 = P2 * V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume."
    },
    {
        "instruction": "Two spheres q1 of charge -16 x 10^(-6)C, q2 of charge -58 x 10^(-6)C are placed at a distance 199 cm. If an uncharged sphere C first comes in contact with A, then with B and placed at 199 cm from both of them, then what is the final force between A and B?\n",
        "input": "Final force between A and B = k * qa * qb / d^2",
        "output": "The final force between spheres A and B can be calculated using the formula F = k * qa * qb / d^2, where k is the electrostatic constant, qa and qb are the charges on A and B respectively, and d is the distance between them. Therefore, the final force between A and B is 6.00e-01 newton\n"
    },
    {
        "instruction": "A wheel starting with an initial angular velocity of 35 rad/s accelerates with a constant angular acceleration of 22 rad/s\u00b2. If it reaches an angular position of 21 rad, then what is its final velocity?",
        "input": "final_angular_velocity = sqrt(initial_angular_velocity^2 + (2 * angular_acceleration * angular_position))",
        "output": "To calculate the final angular velocity, we use the following formula:\n\nfinal_angular_velocity = sqrt(initial_angular_velocity^2 + (2 * angular_acceleration * angular_position))\n\nSubstituting the given values into the formula, we find that the final angular velocity is approximately 46.4 rad/s."
    },
    {
        "instruction": "An Electric motor takes 10 A current, if it consumes 189 J of energy in 98 s, then determine potential difference?",
        "input": "V = Energy / (I * t)",
        "output": "To calculate the potential difference, we use the formula V = Energy / (I * t), where Energy is the energy consumed (189 J), I is the current (10 A), and t is the time (98 s)., this is the final answer 0.2"
    },
    {
        "instruction": "Two point charges q1 = -157 x 10^(-6)C and q2 = -14 x 10^(-6)C are located 87 cm apart in vacuum. What is the electric field at the midpoint O of the line joining two charges?\n",
        "input": "Electric field = (q1 - q2) / (4 * pi * epsilon * r^2)",
        "output": "To calculate the electric field at the midpoint O, we use the formula:\nElectric field = (q1 - q2) / (4 * pi * epsilon * r^2)\nGiven q1 = -157 x 10^(-6)C, q2 = -14 x 10^(-6)C, and r = 87 cm,\nElectric field = 6.80e+06 newton/coulomb\n"
    },
    {
        "instruction": "Find the focal length of a convex mirror whose radius of curvature is 2834.1 cm.",
        "input": "Formula: f = R/2",
        "output": "To find the focal length of a convex mirror, we use the formula f = R/2, where f is the focal length and R is the radius of curvature. By substituting the given value of R into the formula, we can solve for f. In this case, the focal length is 1417.0 cm., this is the final 1417.0"
    },
    {
        "instruction": "A series LCR circuit is connected to a variable frequency 230 V source with L = 186 H, C = 36 muF, R = 132 ohm. Determine the source frequency which drives the circuit in resonance?",
        "input": "Source Frequency = 1 / sqrt(L * C)",
        "output": "12.2 rad/s"
    },
    {
        "instruction": "Two stars each of one solar mass 76000000000000000000000000000000 kg are approaching each other for a head-on collision. When they are at a distance 61000000000 km, their speeds are negligible. What is the speed with which they collide? The radius of each star is 580000 km. Assume the stars remain undistorted until they collide.",
        "input": "Speed = sqrt((-G*m/R) + (G*m/(2*r))) = sqrt(((-6.67 * 10^-11) * 76000000000000000000000000000000) / (61000000000000)) + ((6.67 * 10^-11) * 76000000000000000000000000000000) / (1160000000))",
        "output": "The speed with which the stars collide is approximately 2.09e+06 m/s."
    },
    {
        "instruction": "If a monoatomic gas of 6 moles at 50 atm and volume 17 lit is isothermally changed to pressure 119 atm, then what will be its volume.\n",
        "input": "P1*V1 = P2*V2",
        "output": "7.1lit\nTo determine the final volume of a monoatomic gas after an isothermal expansion, we can use Boyle's Law, which states that for an ideal gas at constant temperature: P1 * V1 = P2 * V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume."
    },
    {
        "instruction": "A small bulb is placed at the bottom of a tank containing liquid to a depth of 100 cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of the liquid is 2.55.",
        "input": "Formula: Area = \u03c0 * h\u00b2 * (k / (1 - k)), where h is the depth of the liquid in centimeters, k is the reciprocal of the refractive index of the liquid, and k = 1 / mu.",
        "output": "This is the answer 0.57 m\u00b2, formula used is : Formula: Area = \u03c0 * h\u00b2 * (k / (1 - k)), where h is the depth of the liquid in centimeters, k is the reciprocal of the refractive index of the liquid, and k = 1 / mu."
    },
    {
        "instruction": "What is the gravitational field at the centre of the uniform solid sphere of radius 527 m and mass 463 kg?",
        "input": "Gravitational Field (g) = cal3(463, 527) N/kg",
        "output": "The gravitational field at the specified point is zero."
    },
    {
        "instruction": "Calculate the torque produced by a 346 N force acting at the end of a 226 m long wrench at an angle of 0 degrees to the wrench.",
        "input": "torque = force * length * sin(angle)",
        "output": "To calculate the torque, we use the following formula:\n\ntorque = force * length * sin(angle)\n\nSubstituting the given values into the formula, we find that the torque is approximately 0.0 Nm."
    },
    {
        "instruction": "In a process, 6638 J of heat is absorbed by a system and 1633 J of work is done on the system. What is the change in internal energy for the process ?\n",
        "input": "\u0394U = Q+W",
        "output": "from first law of thermodynamics, du = q + w => du = (+6638) + (+1633) => du = 8271joule\nQ is positive and W is positive as heat is absorbed by a system and work is done on system."
    },
    {
        "instruction": "A rectangular wire loop of sides 22 cm and 21 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 2.7 T directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is 49 cm/s in a direction normal to the two different sides of the loop? For how long does the induced voltage last in each case?\n",
        "input": "EMF = B * l * v",
        "output": "2.91e-01 volt for 4.49e-01 s if the velocity is perpendicular to the 22 cm side, 2.78e-01 volt for 4.29e-01 s if the velocity is perpendicular to the 21 cm side\n\n\nThe electromotive force (EMF) can be calculated using the formula EMF = B * l * v, where B is the magnetic field magnitude, l is the side length of the rectangular wire loop, and v is the velocity of the loop after conversion from cm/s to m/s."
    },
    {
        "instruction": "A closely wounded solenoid of 800 turns and an area of cross-section 0.0176 m\u00b2 carries a current of 40 A. What is its associated magnetic moment?",
        "input": "n * i * A",
        "output": "The magnetic moment (m) of a solenoid is given by the formula m = n * i * A, where 'n' is the number of turns, 'i' is the current, and 'A' is the area of cross-section. Substituting the given values, we have m = 800 * 40 * 0.0176 = 563.2."
    },
    {
        "instruction": "A convex lens produces a virtual image at a distance of 1130 cm from it of a real object placed 894 cm in front of it. What is the magnification of the lens?",
        "input": "Formula: m = v / u",
        "output": "To calculate the magnification of the lens, we use the formula m = v / u, where m is the magnification, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for m. In this case, the magnification of the lens is 1.3., this is the final The magnification of the lens is 1.3."
    },
    {
        "instruction": "The rear side of a lorry is open and a box of 131 kg mass is placed 7 m away from the open end. The coefficient of friction between the box and the surface below it is 0.82. On a straight road, the lorry starts from rest and accelerates with 13 m/s^2. Will the box move? If yes, at what distance from the starting point does the box fall off the lorry?",
        "input": "Calculate acceleration net, time, and lorry distance",
        "output": "Yes, the box moves with 4.8 m/s^2 with respect to the lorry. It takes 2.9 s to fall off the lorry, and the lorry would have moved 54.7 m by the time the box falls off."
    },
    {
        "instruction": "Two strips of metal are riveted together at their ends by four rivets, each of diameter 9 mm. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed 18549500?",
        "input": "",
        "output": "The maximum tension that can be exerted by the riveted strip is 4.7e+03 newton."
    },
    {
        "instruction": "A raindrop of radius 137 mm falls from a height of 566 m above the ground. It falls with decreasing acceleration until at half its original height, it attains its maximum (terminal) speed, and moves with uniform speed thereafter. What is the work done by the gravitational force on the drop in the first and second half of its journey?",
        "input": "",
        "output": "The work done by the gravitational force on the raindrop can be calculated by using the formula W = (m * g * h) / 2, where m is the mass of the raindrop, g is the acceleration due to gravity, and h is the height. In the first and second half of its journey, the raindrop experiences gravitational force, and the work done by the gravitational force is equal to 29871.9 joules joules., this is the final answer 29871.9 joules"
    },
    {
        "instruction": "An object is placed at 86 cm in front of a convex lens. Image is formed at a distance of 789 cm in front of it. Find the focal length of the lens.",
        "input": "Formula: 1/f = 1/v - 1/u for convex lens.",
        "output": "To find the focal length of the lens, we use the formula for convex lenses: 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for f. In this case, the focal length of the lens is 96.5 cm., this is the final The focal length of the lens is 96.5 cm."
    },
    {
        "instruction": "The piston in the cylinder head of a locomotive has a stroke (3 times the amplitude) of 62 m. If the piston moves with SHM with an angular frequency of 652 rev/min, what its amplitude, maximum speed?\n",
        "input": "amp2 = amp/ratio, v = (freq*amp2)/60",
        "output": "amp2 = amp/ratio, v = (freq*amp2)/60  this is the final answer: amplitude is 2.07e+01 m, its maximum speed is 2.25e+02 ms-1\n"
    },
    {
        "instruction": "A circular disc, of mass 6230 g, is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. If the period of torsional oscillations is 730 ms, and the radius of the disc is 28 cm, determine the torsional spring constant of the wire.",
        "input": "Formula: alpha = (2\u03c0^2 * (m / 1000) * (r / 100)^2) / (t / 1000)^2, where alpha is the torsional spring constant, m is the mass of the disc in grams (6230 g), r is the radius of the disc in centimeters (28 cm), and t is the period of torsional oscillations in milliseconds (730 ms).",
        "output": "Using this formula: Formula: alpha = (2\u03c0^2 * (m / 1000) * (r / 100)^2) / (t / 1000)^2, where alpha is the torsional spring constant, m is the mass of the disc in grams (6230 g), r is the radius of the disc in centimeters (28 cm), and t is the period of torsional oscillations in milliseconds (730 ms)., this is the final answer derived: 1.81e+01 newton-m rad-1"
    },
    {
        "instruction": "Calculate the energy of each of the photons which correspond to light of frequency 754066 Hz.\n",
        "input": "Energy = h*frequency",
        "output": "4.98e-28joules\nTo calculate the energy of a photon, you can use the formula: E = h * f, where E is the energy of the photon, h is the Planck constant (approximately 6.626 x 10^-34 J\u00b7s), and f is the frequency of the light."
    },
    {
        "instruction": "The equilibrium constant for a reaction is 125. Calculate the value of \u0394G^o, given T = 354.9.\n",
        "input": "\u0394G^o = -2.303RTlogK or -RTlnK",
        "output": "-32754.7\nTo calculate the standard Gibbs free energy change (\u0394G^o) for a reaction given the equilibrium constant (K), gas constant (R), and temperature (T), we can use the following equation: \u0394G^o = -R * T * ln(K) where ln represents the natural logarithm."
    },
    {
        "instruction": "A student measures thickness of human hair using a microscope of magnification 178. He makes 217 observations and average width obtained in the field of view of microscope is 3.15 mm. What is the estimate on the thickness of hair?\n",
        "input": "Thickness of hair = Average width in the field of view / Magnification",
        "output": "0.0177 mm\nTo estimate the thickness of a human hair based on the given observations, we can use the following calculation: Thickness of hair = Average width in the field of view / Magnification. In this case, the magnification of the microscope is 178 and the average width obtained in the field of view is 3.15 mm. Substituting these values into the formula, we have: Thickness of hair = 3.15 mm / 178. Calculating this expression will give us the estimate of the thickness of the human hair based on the given observations."
    },
    {
        "instruction": "If a monoatomic gas of 7 moles at 107 atm and volume 191 lit is isothermally changed to pressure 68 atm, then what will be its volume.\n",
        "input": "P1*V1 = P2*V2",
        "output": "300.5lit\nTo determine the final volume of a monoatomic gas after an isothermal expansion, we can use Boyle's Law, which states that for an ideal gas at constant temperature: P1 * V1 = P2 * V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume."
    },
    {
        "instruction": "What is the gravitational force between two masses 35000 kg and 9000 kg seperated bt a distance 88 m.\n",
        "input": "f = (g x m1 x m2)/d^2",
        "output": "the gravitational between two bodies of masses m1 and m2 seperated by a distance d is given by, f = (g x m1 x m2)/d^2 = (6.67 x 10^-11 x 35000 x 10^-3 x 9000 x 10^-3)/88^2 = 2.71e-06 newton\n"
    },
    {
        "instruction": "A long straight wire in the horizontal plane carries a current of of 51 A in south to north direction. What is the magnitude and direction of the magnetic field B at a point 1132 cm west of the wire. (mu = 4 x pi x 10-7 TmA-1)\n",
        "input": "B = (mu * i) / (2 * pi * r)",
        "output": "To calculate the magnitude and direction of the magnetic field B, we use the following formula:\n\nB = (mu * i) / (2 * pi * r)\n\nWhere,\n- B = Magnetic field\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- i = Current flowing through the wire\n- r = Distance from the wire\n\nSubstituting the given values into the formula, we find that the magnitude and direction of the magnetic field B is approximately 9.0e-07 tesla vertically upwards\n."
    },
    {
        "instruction": "A convex lens produces 4 times magnified virtual image of an object at a distance of 8932 cm from the lens. At what distance is the object placed in front of the lens?",
        "input": "Formula: u = v / n",
        "output": "To find the distance at which the object is placed in front of the lens, we use the formula u = v / n, where u is the distance of the object from the lens, v is the distance of the image from the lens, and n is the magnification factor. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 2233.0 cm in front of the lens., this is the final The object is placed at a distance of 2233.0 cm in front of the lens."
    },
    {
        "instruction": "A train, standing in a station-yard, blows a whistle of frequency 632 Hz in still air. The wind starts blowing in the direction from the yard to the station with a speed of 64 ms-1. What is the speed of sound for an observer standing on the station\u2019s platform? Compare it with situation when the air is still and the observer of mass 74 kg runs towards the yard at a speed of 64 ms-1?\n",
        "input": "Apparent frequency = (speed of sound in air/speed of sound in air - speed of train)*original frequency",
        "output": "case-1(wind) : 404 ms-1, case-2(observer) : 340 ms-1\nTo calculate the frequency heard by an observer standing on the station's platform when the wind is blowing, we need to consider the Doppler effect due to the relative motion between the source of sound and the observer. Given that the train blows a whistle of frequency 632 Hz in still air and the wind is blowing in the direction from the yard to the station with a speed of 64 m/s, we can determine the observed frequency for the platform observer.The formula to calculate the observed frequency is: f' = f * (v_sound + v_wind) / (v_sound), where f' is the observed frequency, f is the emitted frequency, v_sound is the speed of sound in still air, and v_wind is the velocity of the wind."
    },
    {
        "instruction": "In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 671 x 10^8 Hz and amplitude 611 V/m. What is the wavelength of the wave?",
        "input": "f = 671 x 10^8 Hz",
        "output": "4.47e-03 m\n\nThe wavelength can be calculated by dividing 3 by the frequency."
    },
    {
        "instruction": "A transverse harmonic wave on a string is described by y(x, t) = 13 sin (98 t + 0.084 x + \u03c0/2) where x and y are in cm and t in s. The positive direction of x is from left to right, then what is the least distance between two successive crests/troughs in the wave?\n",
        "input": "distance = 2*pi/k",
        "output": "74.8 m\nThe distance between two successive crests or troughs in a wave is known as the wavelength (\u03bb). In the given wave equation, y(x, t) = \"+str(amp)+\" sin (\"+str(w)+\" t + \"+str(k)+\" x + \u03c0/\"+str(div)+\"), the wave number (k) is involved in the phase term. The wave number is related to the wavelength by the equation: k = 2\u03c0 / \u03bb"
    },
    {
        "instruction": "Two masses each of mass 99 kg are attached by a spring with K = 185 Nm-1. If a force of 132 N is applied at the free ends of both masses, then what is the time period of oscillation?",
        "input": "Formula: T = 2\u03c0\u221a(m / (2k)), where T is the time period of oscillation, m is the mass of each mass (99 kg), and k is the spring constant (185 Nm-1).",
        "output": "Using this formula: Formula: T = 2\u03c0\u221a(m / (2k)), where T is the time period of oscillation, m is the mass of each mass (99 kg), and k is the spring constant (185 Nm-1)., this is the final answer derived: 3.25e+00 s"
    },
    {
        "instruction": "The far point of a myopic person is 15044 mm in front of the eye. What is the nature and power of the lens required to correct the problem.\n",
        "input": "1/f = 1/v-1/u",
        "output": "the remedial lens should make the objects at infinity appear at far point, hence u = infinity, v = far point of defected eye, from P=1/f, 1/f=1/v-1/u, we get P=1/v-1/u, P=1/v-0=1/v, implies P = 0.07 diatrope, type of lens required is concave.\n"
    },
    {
        "instruction": "9 capacitors each of capacitance 463pF are connected in series. What is the total capacitance of the combination when the system is connected to a 274 V supply?\n",
        "input": "1 / C_total = 1 / C1 + 1 / C2 + 1 / C3 + ... + 1 / Cn\n",
        "output": "5.14e+01 pico-farad\n\nExplanation: 1 / C_total = 1 / 463 + 1 / 463 + 1 / 463 + ... + 1 / 463\n"
    },
    {
        "instruction": "A long straight wire in the horizontal plane carries a current of of 452 A in north to south direction. What is the magnitude and direction of the magnetic field B at a point 540 cm west of the wire. (mu = 4 x pi x 10-7 TmA-1)\n",
        "input": "B = (mu * i) / (2 * pi * r)",
        "output": "To calculate the magnitude and direction of the magnetic field B, we use the following formula:\n\nB = (mu * i) / (2 * pi * r)\n\nWhere,\n- B = Magnetic field\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- i = Current flowing through the wire\n- r = Distance from the wire\n\nSubstituting the given values into the formula, we find that the magnitude and direction of the magnetic field B is approximately 1.7e-05 tesla vertically downwards\n."
    },
    {
        "instruction": "A car weighs 1613 kg. The distance between its front and back axles is 145 m. Its centre of gravity is 98 m behind the front axle. Determine the force exerted by the level ground on each front wheel and each back wheel.",
        "input": "Front Wheel Force = (m * g * (d - x)) / d\nBack Wheel Force = (m * g * x) / d",
        "output": "To calculate the force exerted on the front and back wheels, we use the following formulas:\n\nFront Wheel Force = (m * g * (d - x)) / d\nBack Wheel Force = (m * g * x) / d\n\nWhere,\n- m = Mass of the car\n- g = Acceleration due to gravity\n- d = Distance between front and back axles\n- x = Distance of the car's centre of gravity behind the front axle\n\nSubstituting the given values into the formulas, we find that the force exerted on each front wheel is approximately 5123.8 newtons and the force exerted on each back wheel is approximately 10683.6 newtons."
    },
    {
        "instruction": "If a diatomic gas of 5 moles at 160 atm and volume 122 lit is isothermally changed to volume 94 lit, then what will be the pressure.\n",
        "input": "P1*V1 = P2*V2",
        "output": "207.7atm\nTo determine the final pressure of a diatomic gas after an isothermal expansion, we can use Boyle's Law, which states that for an ideal gas at constant temperature: P1 * V1 = P2 * V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume."
    },
    {
        "instruction": "Monochromatic light of wavelength of 5234 nm is incident on aa surface of refractive index 523.4. What is the wavelength, speed and frequenct of refracted light.\n",
        "input": "speed of light in water = c/refractive index, wavelength = speed of light in water/frequency",
        "output": "1.00e+01 nm , 5.73e+05 m/s and 5.73e+13 hz \nFrequency of light does not depend on the property of the medium in which it is travelling. Hence, the frequency of the refracted ray in water will be equal to the frequency of the incident or reflected light in air."
    },
    {
        "instruction": "What is the lowest total resistance that can be secured by combinations of three coils of resistance 89, 14, 76?",
        "input": "R_total = (R1 * R2 * R3) / (R1 * R2 + R2 * R3 + R3 * R1)",
        "output": "The lowest combination of resistances can be obtained by connecting them in parallel. The total resistance is calculated as (89 * 14 * 76) / (89 * 14 + 14 * 76 + 76 * 89) = 10.4 ohm.\n\nTo calculate the lowest combination of resistances, we connect them in parallel. The total resistance (R_total) is given by the formula (R1 * R2 * R3) / (R1 * R2 + R2 * R3 + R3 * R1), where R1, R2, and R3 are the individual resistances."
    },
    {
        "instruction": "What is the gravitational field at a point P on the surface of the uniform solid sphere of radius 459 m and mass 64 kg?",
        "input": "Gravitational Field (g) = cal3(64, 459) N/kg",
        "output": "The gravitational field at a point P on the surface of the uniform solid sphere of radius 459 m and mass 64 kg is given by the formula g = (-G * m) / (r^2), where G is the gravitational constant, m is the mass, and r is the distance. Plugging in the values, we get g = -2.03e-14 N/kg."
    },
    {
        "instruction": "A person is listening to a tone of 647105 Hz sitting at a distance of 22 m from the source of the sound. What is the time interval between successive compressions from the source?\n",
        "input": "Time interval = Distance / Speed",
        "output": "1.5 microseconds\nTo calculate the time interval between successive compressions from the source, we need to consider the speed of sound in the medium. The speed of sound in air at room temperature is approximately 343 meters per second. The time interval between successive compressions (or any two consecutive points with maximum compression) can be calculated using the formula: Time interval = Distance / Speed. In this case, the distance from the source of the sound is 22 meters and the speed of sound is approximately 343 m/s. Substituting these values into the formula, we can calculate the time interval between successive compressions: Time interval = 22 m / 343 m/s. Calculating this expression will give us the time interval between successive compressions from the source."
    },
    {
        "instruction": "An object of mass 3077 g stands on a weighing machine in a lift, which is moving upwards with a uniform acceleration of 607 cm/s^2.",
        "input": "Scale Reading = m * (10 + (acc / 100))",
        "output": "49.4\nTo calculate the scale reading, we use the formula Scale Reading = mass * (10 + (acceleration / 100)), where the mass is 3077 g and the acceleration is 607 cm/s^2."
    },
    {
        "instruction": "If a diatomic gas of 9 moles at 177 atm and volume 27 lit is adiabatically changed to pressure 53 atm, then what will be its volume.\n",
        "input": "P1*(V1^1.4)=P2*(V2^1.4)",
        "output": "63.9lit\nTo calculate the final pressure of the diatomic gas after an adiabatic expansion, we can use the adiabatic equation: P1 * V1^\u03b3 = P2 * V2^\u03b3, where P1 and V1 are the initial pressure and volume, P2 and V2 are the final pressure and volume, and \u03b3 is the heat capacity ratio. The heat capacity ratio (\u03b3) for a diatomic gas is typically 7/5."
    },
    {
        "instruction": "An Electric Iron takes a current of 8 A, if 1178 J of heat is developed in 7 s, then what is the value of its resistance?",
        "input": "R = energy / (I^2 * t)",
        "output": "To calculate the resistance, we rearrange the formula R = energy / (I^2 * t) to solve for R. Substituting the values, where energy is 1178 J, I is 8 A, and t is 7 s, we can calculate the resistance., this is the final answer 2.6"
    },
    {
        "instruction": "Two amplifiers are connected one after the other in series(cascaded). The first amplifier has a voltage gain of 121 and the second has the voltage gain of 166. If the input signal is 0.05 volt, calculate the output ac signal.\n",
        "input": "V2 = V1*amp1*amp2",
        "output": "If the amplifiers are connected in series, the resultant amplification would be product of amplification factors of each of the amplifer, hence resultant output signal is 121*166*0.05 = 1.00e+03 volt\n"
    },
    {
        "instruction": "An object is projected at an angle 76 from the ground, if the horizontal range of the object is 2851 m, what is the initial velocity of it?",
        "input": "h = 2851 m, theta = 76 degrees",
        "output": "244.0"
    },
    {
        "instruction": "A radioactive isotope has a half-life of 889 years. How long will it take the activity to reduce to 74.2 percent.\n",
        "input": "Time = Half Life/ln2 * ln(Initial Acitivity/Final Activity)",
        "output": "3.83e+02years\nTo calculate the time it takes for the activity of a radioactive isotope to reduce to a certain percentage, we can use the concept of half-life. The half-life (T) is the time it takes for the activity of a radioactive substance to reduce by half. To find the time required to reduce the activity to a certain percentage (p), we can use the formula: t = T * log(0.01) / log(p/100), where t is the time required, T is the half-life, and p is the desired percentage."
    },
    {
        "instruction": "If a point on the circumference of a wheel rotating with an angular acceleration of 839 rad/s\u00b2 has an acceleration of 34 m/s\u00b2, what is the radius of the wheel?",
        "input": "radius = acceleration / angular_acceleration",
        "output": "To calculate the radius, we use the following formula:\n\nradius = acceleration / angular_acceleration\n\nSubstituting the given values into the formula, we find that the radius is approximately 0.0 m."
    },
    {
        "instruction": "A stone is thrown vertically upward with an initial velocity of 30 m/s and reaches a maximum height of 1319 m. After what time does it reach the maximum height?",
        "input": "maximum height (h) = 1319 m, initial velocity (u) = 30 m/s",
        "output": "13.6\nmaximum height (h) = (initial velocity (u) * time (t)) + (0.5 * acceleration (a) * time (t)\u00b2)\nh = (30 * t) + (0.5 * 9.8 * t\u00b2)\nh = 30t + 4.9t\u00b2\n4.9t\u00b2 + 30t - 1319 = 0\n4.9t\u00b2 + 30t - 1319 = 0\n4.9t\u00b2 + 30t = 1319\n4.9t\u00b2 + 30t = 1319\n4.9t\u00b2 + 30t - 1319 = 0\n4.9t\u00b2 + 30t - 1319 = 0\n4.9t\u00b2 + 30t - 1319 = 0\n4.9t\u00b2 + 30t - 1319 = 0\n4.9t\u00b2 + 30t - 1319 = 0\n4.9t\u00b2 + 30t - 1319 = 0\n4.9t\u00b2 + 30t - 1319 = 0\n4.9t\u00b2 + 30t - 1319 = 0\n4.9t\u00b2 + 30t - 1319 = 0\n4.9t\u00b2 + 30t - 1319 = 0\n4.9t\u00b2 + 30t - 1319 = 0\n4.9t\u00b2 + 30t - 1319 = 0\n4.9t\u00b2 + 30t - 1319 = 0"
    },
    {
        "instruction": "A copper block of mass 2737 g is heated in a furnace to a temperature of 500 degree C and then placed on a large ice block. What is the maximum amount of ice that can melt? Specific heat of copper is 0.39 Jg-1\u00b0C-1. Heat of fusion of water = 335 Jg-1.",
        "input": "Maximum amount of ice melted = (mass of block * temperature change * specific heat) / heat of fusion of water",
        "output": "To calculate the maximum amount of ice melted, we use the following formula:\n\nMaximum amount of ice melted = (mass of block * temperature change * specific heat) / heat of fusion of water\n\nSubstituting the given values into the formula, we find that the maximum amount of ice that can melt is approximately 1593.2 g."
    },
    {
        "instruction": "Glycerine flows steadily through a horizontal tube of length 1670 mm and radius 6 cm. If the amount of glycerine collected per second at one end is 513 x 10^(-4) kg/s, what is the pressure difference between the two ends of the tube?",
        "input": "pressure difference = (8 * V * viscosity * length * 100000) / (pi * (radius ** 4))",
        "output": "The pressure difference between the two ends of the tube is 1.07e+01 pascal."
    },
    {
        "instruction": "If a monoatomic gas of 6 moles at 25 atm and volume 163 lit is isothermally changed to pressure 128 atm, then what will be its volume.\n",
        "input": "P1*V1 = P2*V2",
        "output": "31.8lit\nTo determine the final volume of a monoatomic gas after an isothermal expansion, we can use Boyle's Law, which states that for an ideal gas at constant temperature: P1 * V1 = P2 * V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume."
    },
    {
        "instruction": "A circular disc, of mass 11470 g, is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. If the period of torsional oscillations is 700 ms, and the radius of the disc is 24 cm, determine the torsional spring constant of the wire.",
        "input": "Formula: alpha = (2\u03c0^2 * (m / 1000) * (r / 100)^2) / (t / 1000)^2, where alpha is the torsional spring constant, m is the mass of the disc in grams (11470 g), r is the radius of the disc in centimeters (24 cm), and t is the period of torsional oscillations in milliseconds (700 ms).",
        "output": "Using this formula: Formula: alpha = (2\u03c0^2 * (m / 1000) * (r / 100)^2) / (t / 1000)^2, where alpha is the torsional spring constant, m is the mass of the disc in grams (11470 g), r is the radius of the disc in centimeters (24 cm), and t is the period of torsional oscillations in milliseconds (700 ms)., this is the final answer derived: 2.66e+01 newton-m rad-1"
    },
    {
        "instruction": "An object is placed at 574 cm in front of a concave mirror. Image is formed at a distance of 756 cm in front of it. Find the focal length of the mirror.",
        "input": "Formula: 1/f = 1/v + 1/u",
        "output": "To find the focal length of the mirror, we use the formula 1/f = 1/v + 1/u, where f is the focal length, v is the distance of the image, and u is the distance of the object. By substituting the given values into the formula, we can solve for f. In this case, the focal length of the mirror is 326.3 cm., this is the final 326.3"
    },
    {
        "instruction": "A transverse harmonic wave on a string is described by y(x, t) = 26 sin (69 t + 0.117 x + \u03c0/3) where x and y are in cm and t in s. The positive direction of x is from left to right, then what is the least distance between two successive crests/troughs in the wave?\n",
        "input": "distance = 2*pi/k",
        "output": "53.7 m\nThe distance between two successive crests or troughs in a wave is known as the wavelength (\u03bb). In the given wave equation, y(x, t) = \"+str(amp)+\" sin (\"+str(w)+\" t + \"+str(k)+\" x + \u03c0/\"+str(div)+\"), the wave number (k) is involved in the phase term. The wave number is related to the wavelength by the equation: k = 2\u03c0 / \u03bb"
    },
    {
        "instruction": "An Electric motor takes 1 A from a 238 V line. Determine the time taken by it, if it consumes 1554 J of energy?",
        "input": "t = Energy / (V * I)",
        "output": "To calculate the time taken, we use the formula t = Energy / (V * I), where Energy is the energy consumed (1554 J), V is the voltage (238 V), and I is the current (1 A)., this is the final answer 6.5"
    },
    {
        "instruction": "In a Youngs double-slit experiment, the slits are seperated by 0.78 mm and the screen is placed 8.7 m away. The distance between the central bright fringe and the 4 bright fringe is measured to be 2 cm. Determine the wavelength of the ligth used for the experiment.\n",
        "input": "Distance between central bright fringe and bright fringe = (wavelength of light*distance from screen)/distance between slits",
        "output": "4.48e-07 m\nIn a Young's double-slit experiment, the wavelength of light can be determined using the formula: \u03bb = (d * sin(\u03b8)) / n, where \u03bb is the wavelength of light, d is the separation between the slits, \u03b8 is the angle of the fringe (in radians), and n is the order of the fringe."
    },
    {
        "instruction": "Find the focal length of a concave lens whose power is 93.76 D.",
        "input": "Formula: f = 1 / P",
        "output": "To find the focal length of a concave lens, we use the formula f = 1 / P, where f is the focal length and P is the power. By substituting the given value of P into the formula, we can solve for f. In this case, the focal length is 0.0 m., this is the final 0.0"
    },
    {
        "instruction": "An electric appliance of 72636 W power rating is operated in a domestic electric circuit of 226 V that has a current rating of 55.1 A. Will the appliance be safe for a longer time?",
        "input": "P/V - I",
        "output": "It will be safer if P/V - I is less than or equal to 0.01. Now P/V - I = 72636/226 - 55.1 = 266.298. So, it will not be safe for a longer time."
    },
    {
        "instruction": "Suppose the initial charge on the capacitor in an LC circuit with 69 muF capacitor and 104 mH inductor is 46 mC. What is the total energy stored in the circuit initially? What is the total energy at later time?",
        "input": "Initial Energy = 0.5 * Q^2 * (1 / C)",
        "output": "1.53e+01 joule, final value is same as initial value"
    },
    {
        "instruction": "Suppose that the electric field amplitude of an electromagnetic wave is E0 = 1166 N/C and that its frequency is v = 504 MHz. Find an expression for B?",
        "input": "B0 = 3.89e-06 tesla, k = 1.06e+01 rad/m, w = 3.17e+09 rad/s",
        "output": "3.89e-06sin[1.06e+01x-3.17e+09t]\n\nThe expression for the magnetic field (B) of an electromagnetic wave can be written as B = B0sin(kx - wt)."
    },
    {
        "instruction": "Suppose the initial charge on the capacitor in an LC circuit with 46 muF capacitor and 76 mH inductor is 166 mC. What is the total energy stored in the circuit initially? What is the total energy at later time?",
        "input": "Initial Energy = 0.5 * Q^2 * (1 / C)",
        "output": "3.00e+02 joule, final value is same as initial value"
    },
    {
        "instruction": "The mass of a particle is 1.3e-29 kg. If its wavelength is 8.198000000000001e-07 A, calculate its velocity.\n",
        "input": "Velocity = h/wavelength*mass",
        "output": "0.0m/s\nTo find the velocity of the particle, we can use the de Broglie wavelength equation: \u03bb = h / (m * v) where \u03bb is the wavelength, h is the Planck constant (approximately 6.626 x 10^-34 J\u00b7s), m is the mass of the particle, and v is its velocity."
    },
    {
        "instruction": "In a double-slit experiment the angular width of a fringe is found to be 0.2 degrees on a screen placed 3 m away. The wavelength of light used is 26 nm. What will be the angular width of the fringe if the entire experimental apparatus is immersed in liquid of refractive index 1.51.\n",
        "input": "refractive index = angular width before immersing in water/angular width after immersing in water",
        "output": "1.32e-01 degrees\nTo calculate the angular width of a fringe when the entire experimental apparatus is immersed in a liquid of refractive index (\u03bc), we need to consider the effect of the refractive index on the wavelength of light.we can calculate the angular width of the fringe in the liquid (\u03b82') using the formula: \u03b82' = sin^(-1)(\u03bb' / d), where d is the distance to the screen (D) in meters."
    },
    {
        "instruction": "In a chamber, a uniform magnetic field of 0.0086 T is maintained. An electron is shot into the field with a speed of 96000000 m/s, making an angle of 10 degrees with the field. Determine the frequency of the revolution of the electron.",
        "input": "Frequency of revolution = (b * e) / (2 * pi * m)",
        "output": "To calculate the frequency of revolution, we use the following formula:\n\nFrequency of revolution = (b * e) / (2 * pi * m)\n\nSubstituting the given values:\n- b = 0.0086 T\n- e = 1.6000000000000002e-19 C\n- m = 9.1e-31 kg\n\nAfter evaluating the formula, we find that the frequency of revolution is approximately 2.41e+08 sec^-1."
    },
    {
        "instruction": "A hollow cylinder of radius 301 m weighs 32 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 29 m/s. How much work has to be done to stop it?\n",
        "input": "0.5*(1+1)*m*v*v",
        "output": "26912.0 joules\n"
    },
    {
        "instruction": "A convex lens produces a virtual image at a distance of 76 cm from it of a real object having a height of 42 cm and placed 72 cm in front of it. What is the height of the image?",
        "input": "Formula: hi = (v * ho) / u",
        "output": "To find the height of the image, we use the formula hi = (v * ho) / u, where hi is the height of the image, ho is the height of the object, u is the distance of the object from the lens, and v is the distance of the image from the lens. By substituting the given values into the formula, we can calculate hi. In this case, the height of the image is 44.3 cm., this is the final The height of the image is 44.3 cm."
    },
    {
        "instruction": "At what height should an object of mass 452 kg be placed such that its potential energy is 9680 J?",
        "input": "h = PE / (m * g)",
        "output": "To calculate the height, we use the formula h = PE / (m * g), where h is the height, PE is the potential energy (9680 J), m is the mass (452 kg), and g is the acceleration due to gravity (9.8 m/s^2)., this is the final answer 2.2"
    },
    {
        "instruction": "A meter stick is balanced on a knife edge at its center. When two coins, each of mass 38 g and 12 g respectively, are put at the 36 mark and 93 mark respectively, the stick is found to be balanced at 78 cm. What is the mass of the meter stick?",
        "input": "Mass = (Right Side - Left Side) / Distance",
        "output": "The mass of the meter stick is approximately -50.6 g.\nLeft Side = m1 * (t3 - t1) = 38 * (78 - 36)\nRight Side = m2 * (t2 - t3) = 12 * (93 - 78)"
    },
    {
        "instruction": "A girl sitting on a merry-go-round is moving in a counter-clockwise arc length of 669 m. If the angular displacement is 557 rad, how far is she from the center of the merry-go-round?",
        "input": "distance_from_center = arc_length / radius",
        "output": "To calculate the distance from the center, we use the following formula:\n\ndistance_from_center = arc_length / radius\n\nSubstituting the given values into the formula, we find that the distance from the center is approximately 1.2 m."
    },
    {
        "instruction": "Distance of a spaceship from the ground station is 157972.4 km, then in what time will a signal from the ground station reach the spaceship? (Signal travels with the speed of light)",
        "input": "s = 157972.4 km",
        "output": "The time taken for the signal to reach the spaceship is 526.6 ms."
    },
    {
        "instruction": "The water pressure at the bottom of the trench is about 4976 x 10^4 Pa. A steel ball of initial volume 991 dm^3 is dropped into the ocean and falls to the bottom of the trench. What is the change in the volume of the ball when it reaches the bottom?",
        "input": "volume_change = (pressure * 10 * initial_volume) / (1.6 * 10^11)",
        "output": "The change in volume of the steel ball when it reaches the bottom of the trench is approximately 3.1e-04 m^3. We can calculate the volume change using the formula:\n\nvolume_change = (pressure * 10 * initial_volume) / (1.6 * 10^11)"
    },
    {
        "instruction": "A square coil of side 16 cm consists of 26 turns and carries a current of 20 A. The coil is suspended vertically, and the normal to the plane of the coil makes an angle of 44 degrees with the direction of a uniform horizontal magnetic field of magnitude 6 tesla. What is the magnitude of the torque experienced by the coil.",
        "input": "Torque = n * b * i * A * sin(d)",
        "output": "To calculate the magnitude of the torque experienced by the coil, we use the following formula:\n\nTorque = n * b * i * A * sin(d)\n\nWhere,\n- n = Number of turns in the coil\n- b = Magnetic field\n- i = Current in the coil\n- A = Area of the coil\n- d = Angle between the normal to the coil and the magnetic field\n\nFor a square coil, the area (A) is equal to the square of the side length (l) of the coil. For a circular coil, the area (A) is equal to pi times the square of the radius (l) of the coil.\n\nSubstituting the given values into the formula and evaluating it, we find that the magnitude of the torque experienced by the coil is approximately 55.5 newton-m."
    },
    {
        "instruction": "A bullet of mass 2 kg and horizontal speed 74 m/s strikes a block of wood of mass 59 kg and instantly comes to rest with respect to the block. The block is suspended from the ceiling by a thin wire. Calculate the height to which the block rises.",
        "input": "h = (v^2) / (2 * g)",
        "output": "To calculate the height, we use the formula h = (v^2) / (2 * g), where h is the height, v is the velocity of the bullet after the collision, and g is the acceleration due to gravity (9.8 m/s^2)., this is the final answer 0.3"
    },
    {
        "instruction": "If a diatomic gas of 10 moles at 19 m3 is isothermally changed to volume 51 m3 at 58 K, then what is the work done.\n",
        "input": "Work Done = n*R*T*ln(V2/V1)",
        "output": "-4759.0 joules\nTo calculate the work done during an isothermal expansion of a diatomic gas, we can use the following equation: Work done = n * R * T * ln(V2/V1), where n is the number of moles of the gas, R is the ideal gas constant (approximately 8.314 J/(mol\u00b7K)), T is the temperature in Kelvin, V1 is the initial volume, and V2 is the final volume."
    },
    {
        "instruction": "A copper wire has a cross-sectional area of 3 m\u00b2 and resistivity of 50 ohm-m. What is the length of this wire that makes its resistance 45 ohm?",
        "input": "R = 45 ohm, A = 3 m\u00b2, rho = 50 ohm-m",
        "output": "The length of the wire required to achieve a resistance of 45 ohm is 2.7 m. It is calculated by dividing the product of resistance and area (135) by the resistivity (50)."
    },
    {
        "instruction": "What is the electric field at a point P at a distance of 254 m from the center of the spherical shell of radius 198 m and having 1.73e-06 C charge distributed uniformly on it?",
        "input": "Electric Field (E) = cal2(1.73e-06, 254, 198) N/C",
        "output": "2.41e-01 newton/coulomb\nThe electric field due to a uniformly charged spherical shell is given by the formula E = k * Q * r / (R^2), where k is the Coulomb's constant, Q is the charge on the shell, r is the distance from the center of the shell, and R is the radius of the shell. Plugging in the values, we get E = 2.41e-01 N/C."
    },
    {
        "instruction": "Calculate the charge (in C) of 3.57e+18 electrons?",
        "input": "Q = n * e",
        "output": "6.00e-01 coulomb\n\nThe charge of electrons can be calculated using the formula: Q = n * e, where n is the number of electrons and e is the charge of an electron."
    },
    {
        "instruction": "A transverse harmonic wave on a string is described by y(x, t) = 31 sin (33 t + 0.065 x + \u03c0/3) where x and y are in cm and t in s. The positive direction of x is from left to right, then what is the initial phase at the origin?\n",
        "input": "distance = 2*pi/k",
        "output": "\u03c0/3\nTo determine the initial phase, we look at the phase term in the equation, which is \"+str(k)+\"x + \u03c0/\"+str(div)+\". At the origin (x=0), the phase term becomes \"+str(\"\u03c0/\"+str(div))+\". Hence, the initial phase at the origin is \"+str(\"\u03c0/\"+str(div))+\" radians or \"+str(\"180/\"+str(div))+\" degrees."
    },
    {
        "instruction": "Suppose there existed a planet that went around the Sun 1523/1460 times as fast as the Earth. What would be its orbital size as compared to that of the Earth?",
        "input": "Orbital Size Ratio = (T_p / T_e)^(2/3) = (1523/1460)^(2/3)",
        "output": "The orbital size of the planet compared to that of the Earth would be approximately 1.0 times faster than Earth."
    },
    {
        "instruction": "A sound produces 1896 crests and 1896 troughs in 9 seconds. When the first trough is produced, the first crest is 1550 m away from the source, then calculate the frequency ?\n",
        "input": "Wavelength = Speed*Time Period, ",
        "output": "210.7 hz\nTo calculate the speed of sound, we need to determine the distance traveled by a crest or trough in the given time interval. In 9 seconds, 1896 crests and 1896 troughs are produced. This means that one complete cycle of the wave (a crest and a trough) occurs 1896 times in 9 seconds. Therefore, the time taken for one complete cycle (T) can be calculated as: T = 9 s / 1896 cycles. The distance traveled by one complete cycle (wavelength, \u03bb) is given by the formula: \u03bb = speed * T, where speed is the speed of sound. Since the first crest is 1550 m away from the source, the distance traveled by a complete cycle (\u03bb) can be expressed as: \u03bb = 1550 m + 1550 m = 2 * 1550 m. Substituting the value of \u03bb and T into the equation, we can calculate the speed of sound: speed = \u03bb / T = (2 * 1550 m) / (9 s / 1896 cycles). Calculating this expression will give us the speed of sound."
    },
    {
        "instruction": "Estimate the fraction of molecular volume to the actual volume occupied by a gas at STP. Take the diameter of the gas molecule to be 928.3 A and volume occupied by a gas at STP as 22.4 L.",
        "input": "(4 * pi * d * d * d * 1000 * n) / (3 * 8 * 22.4)",
        "output": "1.126233700067059e+34 \n (4 * pi * d * d * d * 1000 * n) / (3 * 8 * 22.4)"
    },
    {
        "instruction": "Current in a circuit falls from 194 A to 5 A in 0.13 s. If an average emf of 177 V induced, give an estimate of the self-inductance of the circuit.\n",
        "input": "Self-Inductance = (Average EMF * Time) / (Initial Current - Final Current)",
        "output": "1.22e-01 henry\n\n\nThe self-inductance of the circuit can be estimated using the formula Self-Inductance = (Average EMF * Time) / (Initial Current - Final Current), where Average EMF is the average induced electromotive force, Time is the time taken for the current to change, Initial Current is the initial current in the circuit, and Final Current is the final current in the circuit."
    },
    {
        "instruction": "An image is formed by a convex lens of focal length 311 cm at a distance of 441 cm behind it. Find at what distance object is placed in front of lens.",
        "input": "Formula: 1/f = 1/v - 1/u for convex lens.",
        "output": "To find the distance of the object from the lens, we use the formula for convex lenses: 1/f = 1/v - 1/u, where f is the focal length ofthe lens, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 1055.0 cm from the lens., this is the final The object is placed at 1055.0 cm in front of the lens."
    },
    {
        "instruction": "Two objects of masses 4 g and 14 g are moving along the same line and direction with velocities of 15 m/s and 2 m/s respectively. They collide and after the collision, the first object moves at a velocity of 12 m/s. Determine the initial velocity of the first object.",
        "input": "u1 = ((m1 * v1) + (m2 * v2) - (m2 * u2)) / m1",
        "output": "To find the initial velocity of the first object (u1), we use the formula:\n\nu1 = ((m1 * v1) + (m2 * v2) - (m2 * u2)) / m1\n\nSubstituting the given values, we have:\n\nu1 = ((4 * 12) + (14 * 28) - (14 * 2)) / 4\n\nSimplifying the expression gives us u1 = 57.5 m/s."
    },
    {
        "instruction": "If a point on the circumference of a wheel rotating with an angular acceleration of 263 rad/s\u00b2 has an acceleration of 648 m/s\u00b2, what is the radius of the wheel?",
        "input": "radius = acceleration / angular_acceleration",
        "output": "To calculate the radius, we use the following formula:\n\nradius = acceleration / angular_acceleration\n\nSubstituting the given values into the formula, we find that the radius is approximately 2.5 m."
    },
    {
        "instruction": "A sonar device on a submarine sends out a signal and receives an echo 317 s later. Find the speed of sound in that material if the distance of the object from the submarine is 4583 m ?\n",
        "input": "Distance = Speed * Time",
        "output": "28.9 m/s\nTo find the speed of sound in the material, we can use the equation: Speed = Distance / Time. In this case, the distance of the object from the submarine is 4583 meters and the time it takes for the echo to return is 317 seconds. Substituting these values into the equation, we can calculate the speed of sound in the material: Speed = 4583 m / 317 s. Calculating this expression will give us the speed of sound in the material."
    },
    {
        "instruction": "A long straight wire in the horizontal plane carries a current of of 341 A in west to east direction. What is the magnitude and direction of the magnetic field B at a point 1191 cm north of the wire.\n",
        "input": "B = (mu * i) / (2 * pi * r)",
        "output": "To calculate the magnitude and direction of the magnetic field B, we use the following formula:\n\nB = (mu * i) / (2 * pi * r)\n\nWhere,\n- B = Magnetic field\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- i = Current flowing through the wire\n- r = Distance from the wire\n\nSubstituting the given values into the formula, we find that the magnitude and direction of the magnetic field B is approximately 5.7e-06 tesla vertically upwards\n."
    },
    {
        "instruction": "A convex lens produces a real image of height 182 cm of a real object of height 444 cm placed in front of it. What is the magnification of the lens?",
        "input": "Formula: m = hi / ho",
        "output": "To calculate the magnification of the lens, we use the formula m = hi / ho, where m is the magnification, hi is the height of the image, and ho is the height of the object. By substituting the given values into the formula, we can solve for m. In this case, the magnification of the lens is 0.4., this is the final The magnification of the lens is 0.4."
    },
    {
        "instruction": "A hoop of mass 6099 kg has a radius of 81 m. What is the moment of inertia with respect to its symmetric axis?",
        "input": "Moment of Inertia = (Constant) * mass * radius^2",
        "output": "The moment of inertia with respect to its symmetric axis is approximately 40015539 kgm^2.\n\nMoment of Inertia = (Constant) * mass * radius^2\n\nConstant = 1\nmass = 6099 kg\nradius = 81 m"
    },
    {
        "instruction": "A steam engine delivers 344 J of work per minute and services 1081 J of heat per minute from its boiler. What is the efficiency of the engine?\n",
        "input": "Efficiency = Work per minute/Heat per minute from its boiler",
        "output": "31.8\nThe efficiency of an engine can be calculated using the formula: Efficiency = (Work output / Heat input) * 100"
    },
    {
        "instruction": "A polythene is rubbed with wool is found to have a negative charge of 854737 x 10^(-12) C. Estimate the number of electrons transferred (from which to which)?\n",
        "input": "Number of electrons = (charge / elementary charge)",
        "output": "To estimate the number of electrons transferred, we use the formula:\nNumber of electrons = (charge / elementary charge)\nGiven charge = 854737 x 10^(-12) C and elementary charge = 1.6 x 10^(-19) C,\nNumber of electrons = 5.342e+12 electrons transfered from wool to polythene\n"
    },
    {
        "instruction": "At t = 0, a wheel is rotating with an angular velocity of 469 rad/s at a constant angular acceleration of 24 rad/s\u00b2. It attains an angular velocity of w rad/s in t = 22 sec. What is the value of the final angular velocity?",
        "input": "final_angular_velocity = initial_angular_velocity + (angular_acceleration * time)",
        "output": "To calculate the final angular velocity, we use the following formula:\n\nfinal_angular_velocity = initial_angular_velocity + (angular_acceleration * time)\n\nSubstituting the given values into the formula, we find that the final angular velocity is approximately 997 rad/s."
    },
    {
        "instruction": "A closely wounded solenoid 367 cm long has 2 layers of windings of 450 turns each. The diameter of the solenoid is d cm. If the current carried is 43 A, estimate the magnitude of the magnetic field inside the solenoid near its center.",
        "input": "B = (mu * n * i) / l",
        "output": "To estimate the magnitude of the magnetic field inside the solenoid near its center, we use the following formula:\n\nB = (mu * n * i) / l\n\nWhere,\n- B = Magnetic field inside the solenoid near its center\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- n = Number of turns per layer\n- i = Current flowing through the solenoid\n- l = Length of the solenoid\n\nSubstituting the given values into the formula, we find that the magnitude of the magnetic field inside the solenoid near its center is approximately 6.63e-03 tesla."
    },
    {
        "instruction": "Two masses each of mass 196 kg are attached by a spring with K = 46 Nm-1. If a force of 17 N is applied at the free ends of both masses, then what is the time period of oscillation?",
        "input": "Formula: T = 2\u03c0\u221a(m / (2k)), where T is the time period of oscillation, m is the mass of each mass (196 kg), and k is the spring constant (46 Nm-1).",
        "output": "Using this formula: Formula: T = 2\u03c0\u221a(m / (2k)), where T is the time period of oscillation, m is the mass of each mass (196 kg), and k is the spring constant (46 Nm-1)., this is the final answer derived: 9.17e+00 s"
    },
    {
        "instruction": "A 43 kg mass, fastened to the end of a steel wire of initial length 26 m, is whirled in a vertical circle with an angular velocity of 2 rev/s at the bottom of the circle. The cross-sectional area of the wire is 65 mm^2. Calculate the elongation of the wire when the mass is at the lowest point of its path.",
        "input": "elongation = (force * length) / (A * 10^(-6) * Y_steel)",
        "output": "To calculate the elongation, we use the formula:\n\nelongation = (force * length) / (A * 10^(-6) * Y_steel)\n = (43 kg * (9.8 + 26 m * \u03c0^2 * 2^2) * 26 m) / (65 mm^2 * 10^(-6) m^2 * (2 * 10^11 N/m^2))\n = 8.9 cm."
    },
    {
        "instruction": "Calculate the energy of each of the photons which have wavelength of 69500 nm. (h = 6.6 * 10^-34 Js, c = 3 * 10^8 m/s)\n",
        "input": "E = 6.6*10^-34 * c/wavelength",
        "output": "2.85e-21joules\nTo calculate the energy of a photon, you can use the formula: E = h * c/lambda, where E is the energy of the photon, h is the Planck constant (approximately 6.626 x 10^-34 J\u00b7s), c is the speed of light and lambda is the wavelength of the light."
    },
    {
        "instruction": "An object is placed at 555 cm in front of a concave mirror. Image is formed at a distance of 997 cm in front of it. Find the focal length of the mirror.",
        "input": "Formula: 1/f = 1/v + 1/u",
        "output": "To find the focal length of the mirror, we use the formula 1/f = 1/v + 1/u, where f is the focal length, v is the distance of the image, and u is the distance of the object. By substituting the given values into the formula, we can solve for f. In this case, the focal length of the mirror is 356.5 cm., this is the final 356.5"
    },
    {
        "instruction": "A copper block of mass 1438 g is heated in a furnace to a temperature of 902 degree C and then placed on a large ice block. What is the maximum amount of ice that can melt? Specific heat of copper is 0.91 Jg-1\u00b0C-1. Heat of fusion of water = 335 Jg-1.",
        "input": "Maximum amount of ice melted = (mass of block * temperature change * specific heat) / heat of fusion of water",
        "output": "To calculate the maximum amount of ice melted, we use the following formula:\n\nMaximum amount of ice melted = (mass of block * temperature change * specific heat) / heat of fusion of water\n\nSubstituting the given values into the formula, we find that the maximum amount of ice that can melt is approximately 3523.4 g."
    },
    {
        "instruction": "A long straight wire in the horizontal plane carries a current of of 273 A in east to west direction. What is the magnitude and direction of the magnetic field B at a point 1094 cm south of the wire. (mu = 4 x pi x 10-7 TmA-1)\n",
        "input": "B = (mu * i) / (2 * pi * r)",
        "output": "To calculate the magnitude and direction of the magnetic field B, we use the following formula:\n\nB = (mu * i) / (2 * pi * r)\n\nWhere,\n- B = Magnetic field\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- i = Current flowing through the wire\n- r = Distance from the wire\n\nSubstituting the given values into the formula, we find that the magnitude and direction of the magnetic field B is approximately 5.0e-06 tesla vertically upwards\n."
    },
    {
        "instruction": "A closely wounded solenoid 994 cm long has 10 layers of windings of 500 turns each. The diameter of the solenoid is d cm. If the current carried is 2 A, estimate the magnitude of the magnetic field inside the solenoid near its center.",
        "input": "B = (mu * n * i) / l",
        "output": "To estimate the magnitude of the magnetic field inside the solenoid near its center, we use the following formula:\n\nB = (mu * n * i) / l\n\nWhere,\n- B = Magnetic field inside the solenoid near its center\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- n = Number of turns per layer\n- i = Current flowing through the solenoid\n- l = Length of the solenoid\n\nSubstituting the given values into the formula, we find that the magnitude of the magnetic field inside the solenoid near its center is approximately 1.26e-04 tesla."
    },
    {
        "instruction": "Two circular coils X and Y of radii 13 cm and 24 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil A has 11 turns and carries a current of 32 A, Coil B has 2 turns and carries a current of 32 A. The sense of current in X is anti-clockwise direction and in Y is clockwise direction. From an observer looking at the coils facing east, give the magnitude and direction of the net magnetic field due to the coils at the center.",
        "input": "Net magnetic field = |b1 - b2|",
        "output": "To calculate the net magnetic field, we use the following formula:\n\nNet magnetic field = |b1 - b2|\n\nWhere,\n- b1 = Magnetic field due to coil X\n- b2 = Magnetic field due to coil Y\n\nWe calculate the magnetic field for each coil using the formula:\n- Magnetic field due to coil X = (mu * n1 * i1) / (2 * r1)\n- Magnetic field due to coil Y = (mu * n2 * i2) / (2 * r2)\n\nSubstituting the given values and evaluating the formula, we find that the magnitude of the net magnetic field is approximately 1.53e-03 tesla and towards east."
    },
    {
        "instruction": "A large steel wheel is to be fitted onto a shaft of the same material. At 120 degree C, the outer diameter of the shaft is 103 cm and the diameter of the central hole in the wheel is 102.989 cm. The shaft is cooled using 'dry ice'. At what temperature of the shaft does the wheel slip on the shaft? Assume the coefficient of linear expansion of the steel to be constant over the required temperature range \u03b1steel = 1.20 x 10-5K-1.",
        "input": "Required temperature = t1 + ((d2 - d1) / (\u03b1 * d1))",
        "output": "To calculate the required temperature, we use the following formula:\n\nRequired temperature = t1 + ((d2 - d1) / (\u03b1 * d1))\n\nSubstituting the given values into the formula, we find that the temperature is approximately 113.7 degree C."
    },
    {
        "instruction": "Suppose that the electric field part of an electromagnetic wave in vacuum is E = 708cos[99y + 3030303t]. What is the amplitude of the magnetic field part of the wave?",
        "input": "E0 = 708 N/C",
        "output": "2.36e-06 tesla\n\nThe magnetic field amplitude can be calculated by dividing the electric field amplitude by the speed of light."
    },
    {
        "instruction": "The peak voltage of an ac supply is 1950956 mV. What is the rms voltage?",
        "input": "RMS Voltage = Peak Voltage / sqrt(2)",
        "output": "1.380e+03 volt"
    },
    {
        "instruction": "Calculate the energy of each of the photons which have wavelength of 191754 nm.\n",
        "input": "Energy = h*c/wavelength",
        "output": "1.03e-21joules\nTo calculate the energy of a photon, you can use the formula: E = h * c/lambda, where E is the energy of the photon, h is the Planck constant (approximately 6.626 x 10^-34 J\u00b7s), c is the speed of light and lambda is the wavelength of the light."
    },
    {
        "instruction": "Calculate the energy of each of the photons which correspond to light of frequency 643913 Hz. (h = 6.6 * 10^-34 Js)\n",
        "input": "E = 6.6*10^-34 * frequency",
        "output": "4.25e-28joules\nTo calculate the energy of a photon, you can use the formula: E = h * f, where E is the energy of the photon, h is the Planck constant (approximately 6.626 x 10^-34 J\u00b7s), and f is the frequency of the light."
    },
    {
        "instruction": "A concave mirror produces 86 times diminished real image of an object at a distance of 24.46 cm from the mirror. At what distance is the object placed in front of the mirror?",
        "input": "Formula: u = v * n",
        "output": "To find the distance at which the object is placed in front of the mirror, we use the formula u = v * n, where u is the distance of the object from the mirror, v is the distance of the image from the mirror, and n is the magnification factor. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 2103.6 cm in front of the mirror., this is the final The object is placed at a distance of 2103.6 cm in front of the mirror."
    },
    {
        "instruction": "A circuit consists of 16 V battery, 127 ohm resistance, then what is the time taken to produce 751 J of energy in the circuit?",
        "input": "t = (energy * R) / (V^2)",
        "output": "To calculate the time taken, we rearrange the formula t = (energy * R) / (V^2) to solve for t. Substituting the values, where energy is 751 J, R is 127 ohm, and V is 16 V, we can calculate the time., this is the final answer 372.6"
    },
    {
        "instruction": "On a two-lane road, car A is traveling with a speed of 55 m/s. Two cars B and C approach car A in opposite directions with a speed of 125 m/s each. At a certain instant, when the distance AB is equal to AC, both being 94 km, B decides to overtake A before C does. What minimum acceleration of car B is required to avoid an accident?",
        "input": "relative speed of A with respect to C = v1 + v2, relative speed of B with respect to A = v2 - v1, time taken by C to cover distance AC = distance / relative speed of A with respect to C, minimum acceleration required = (2 * (distance - relative speed of B with respect to A * time)) / (time ** 2)",
        "output": "relative speed of A with respect to C is 180 m/s, B with respect to A is 70 m/s, time taken by C to cover distance AC is 522.2 s, minimum acceleration required is 0.4 m/s\u00b2\n\nrelative speed of A with respect to C = v1 + v2, relative speed of B with respect to A = v2 - v1, time taken by C to cover distance AC = distance / relative speed of A with respect to C, minimum acceleration required = (2 * (distance - relative speed of B with respect to A * time)) / (time ** 2)\n\n\n\nThe relative speed of A with respect to C is the sum of the speeds of A and C. The relative speed of B with respect to A is the difference between the speeds of B and A. The time taken by C to cover the distance AC is the distance AC divided by the relative speed of A with respect to C. The minimum acceleration required is the acceleration of B required to cover the distance AB in the time interval of time taken by C to cover the distance AC minus the time taken by B to cover the distance AB."
    },
    {
        "instruction": "A small bulb is placed at the bottom of a tank containing liquid to a depth of 190 cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of the liquid is 2.4.",
        "input": "Formula: Area = \u03c0 * h\u00b2 * (k / (1 - k)), where h is the depth of the liquid in centimeters, k is the reciprocal of the refractive index of the liquid, and k = 1 / mu.",
        "output": "This is the answer 2.38 m\u00b2, formula used is : Formula: Area = \u03c0 * h\u00b2 * (k / (1 - k)), where h is the depth of the liquid in centimeters, k is the reciprocal of the refractive index of the liquid, and k = 1 / mu."
    },
    {
        "instruction": "On an unknown scale, the temperature of the melting point and boiling point of water is 29 degrees and 177 degrees respectively. If the temperature on the Kelvin scale is 315 degrees Kelvin, what is the temperature shown on that scale?",
        "input": "Temperature on the unknown scale = (((t2 - t1) * (t - ta)) / (tb - ta)) + t1",
        "output": "To find the temperature on the unknown scale, we use the following formula:\n\nTemperature on the unknown scale = (((t2 - t1) * (t - ta)) / (tb - ta)) + t1\n\nSubstituting the given values into the formula, we find that the temperature on the unknown scale is approximately 91.2."
    },
    {
        "instruction": "Light enters from a material-1 having refractive index 2.2 to material-2 having refractive index 5.7. If the speed of light in material-2 is 288900000 m/s, what is the speed of light in material-1?",
        "input": "Speed of Light in a Material (v) = (n1 * c) / n2",
        "output": "The speed of light in a material can be calculated using the formula v = (n1 * c) / n2, where v is the speed of light in the material, n1 is the refractive index of material-1, c is the speed of light in vacuum, and n2 is the refractive index of material-2., this is the final 748513636.4 m/s"
    },
    {
        "instruction": "A bar magnet of magnetic moment 1.21 J/T is kept in a uniform magnetic field of 0.08 T. What is the work done by an external torque to turn the magnet which is aligned at an angle of 55 degrees with the magnetic field to an angle of 56 degrees?",
        "input": "-m * b * (d1 - d2)",
        "output": "The work done by an external torque to turn the magnet aligned at an angle of 0.573576436351046 degrees with the magnetic field to an angle of 0.5591929034707468 degrees can be calculated using the formula -m * b * (d1 - d2), where 'm' is the magnetic moment of the magnet, 'b' is the magnetic field strength, 'd1' is the initial angle, and 'd2' is the final angle. Substituting the given values, we have -(1.21) * 0.08 * (0.57 - 0.56)."
    },
    {
        "instruction": "A 954 pF capacitor is connected to a 1267 V battery. How much electrostatic energy is stored in the capacitor?",
        "input": "Formula: 0.5 * 954 * 1267^2 * 10^(-12)\nValues: c = 954 pF, v = 1267 V",
        "output": "Answer:7.66e-04 joule\n\nExplanation: The electrostatic energy stored in the capacitor can be calculated using the formula:\n\nE = 0.5 * C * V^2\n\nwhere C is the capacitance (in Farads) and V is the voltage (in volts).\n\nSubstituting the given values, we have:\n\nE = 0.5 * 954 pF * 1267^2 * 10^(-12) = 7.66e-04 joule joule."
    },
    {
        "instruction": "A body of mass 188 kg is acted upon by two perpendicular forces 35 N and 131 N. Give the magnitude and direction of the acceleration of the body.",
        "input": "",
        "output": "0.7 ms-2, 75 degrees with 35 newton force"
    },
    {
        "instruction": "If current flowing through a conductor is 442 A, then what is the charge flown through the conductor in 108 s?",
        "input": "Q = I * t",
        "output": "4.77e+04 coulomb\n\nThe charge flown through the conductor can be calculated using the formula: Q = I * t, where I is the current and t is the time."
    },
    {
        "instruction": "Torque of 883 Nm is transmitted to an engine at a power of 97 W. What is the angular speed of the rotor?",
        "input": "Angular Speed = Power / Torque",
        "output": "Angular Speed = 97 W / 883 Nm\n\nTo calculate the angular speed of the rotor, we use the following formula:\n\nAngular Speed = Power / Torque\n\nSubstituting the values:\n\nPower = 97 W\nTorque = 883 Nm\n\nWe find that the angular speed of the rotor is 0.1 rad/s."
    },
    {
        "instruction": "An oxygen cylinder of volume 31 litre has an initial gauge pressure of 16 atmosphere and a temperature of 31 degree C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 6 atmosphere and its temperature drops to 54 degree C. Estimate the number of moles of oxygen taken out of the cylinder.",
        "input": "n = (p1 * V) / (R * T1) - (p2 * V) / (R * T2)",
        "output": "12.8 mol \n \np1 = initial pressure\np2 = final pressure\nV = volume\nt1 = initial temperature\nt2 = final temperature\nR = gas constant\nn = (16 * 31 * 10^5) / (8.31 * 304) - (6 * 31 * 10^5) / (8.31 * 327)\nn = 19633.9 - 6844.9\nn = 12789.1\nn = 12.8 mol"
    },
    {
        "instruction": "A meter stick is balanced on a knife edge at its center. Where will the stick be balanced when two coins, each of mass 94 g and 8 g respectively, are put at the 3 mark and 82 mark respectively?",
        "input": "Balance Position = ((50 * m) + (m1 * t1) + (m2 * t2)) / (m + m1 + m2)",
        "output": "The stick will be balanced at approximately 26.7 cm.\nBalance Position = ((50 * 77) + (94 * 3) + (8 * 82)) / (77 + 94 + 8)"
    },
    {
        "instruction": "Calculate the torque produced by a 253 N force acting at the end of a 248 m long wrench at an angle of 1.5707963267948966 degrees to the wrench.",
        "input": "torque = force * length * sin(angle)",
        "output": "To calculate the torque, we use the following formula:\n\ntorque = force * length * sin(angle)\n\nSubstituting the given values into the formula, we find that the torque is approximately 1719.9 Nm."
    },
    {
        "instruction": "Two objects collide and their masses are unknown. Their initial velocities are 8 m/s and 30 m/s respectively. After the collision, the first object moves at a velocity of 16 m/s and the second object moves at a velocity of 6 m/s. Determine the mass of the first object.",
        "input": "m1 = (m2 * (v2 - u2)) / (u1 - v1)",
        "output": "To find the mass of the first object (m1), we use the formula:\n\nm1 = (m2 * (v2 - u2)) / (u1 - v1)\n\nSubstituting the given values, we have:\n\nm1 = (2 * (6 - 30)) / (8 - 16)\n\nSimplifying the expression gives us m1 = 6.0 g."
    },
    {
        "instruction": "A parallel plate capacitor made of circular plates of radius r = 87 cm has a capacitance C = 35 pF. The capacitor is connected to a 230 V ac supply with an angular frequency of 110 rad/s. Determine the amplitude of B at a point 3 cm from the axis between the plates?",
        "input": "d = 3 cm, r = 87 cm, I = 8.86e-07 ampere",
        "output": "9.93e-15 tesla\n\nThe amplitude of the magnetic field at a point between the plates can be calculated using the formula: B = (\u03bc\u2080dI\u2080) / (r\u00b2), where \u03bc\u2080 is the permeability of free space, d is the distance from the axis, I\u2080 is the rms current, and r is the radius of the plates."
    },
    {
        "instruction": "A hollow sphere rolls down two different inclined planes of heights 12 cm and 15 cm and with angles of inclination of 62 and 24, on which it reaches the bottom with more speed?",
        "input": "speed = height / (k + 1)",
        "output": "To compare the speeds, we use the following formula:\n\nspeed = height / (k + 1)\n\nSubstituting the given values into the formula, we find that:\n\nThe second plane has more speed."
    },
    {
        "instruction": "A force of 809 N acts on an object. The displacement is 342 m in the direction of the force, then what is the work done by this force?",
        "input": "W = F * s",
        "output": "Using the formula: W = F * s, the final answer is: {'answer': '276678 J', 'explanation': 'To calculate the work done by a force, we use the formula W = F * s, where W is the work done, F is the force (809 N), and s is the displacement (342 m).'}"
    },
    {
        "instruction": "What is the electric field at a point P on the surface of the spherical shell of radius 588 m and having 4.20e-07 C charge distributed uniformly on it?",
        "input": "Electric Field (E) = cal3(4.20e-07, 588) N/C",
        "output": "1.09e-02 newton/coulomb\nThe electric field on the surface of a uniformly charged spherical shell is given by the formula E = k * Q / (R^2), where k is the Coulomb's constant, Q is the charge on the shell, and R is the radius of the shell. Plugging in the values, we get E = 1.09e-02 N/C."
    },
    {
        "instruction": "Suppose we employ a system of units in which the unit of mass equals 69 kg, the unit of length equals 53 m, the unit of time is 45 s, if the value of x newton is equal to 7 units in new system, find x?\n",
        "input": "x N = (m kg) * (l m) / (t^2 s^2)",
        "output": "12.64\nTo find the value of x newtons in the given system of units, we need to consider the relationships between the units of mass (kg), length (m), time (s), and force (Newton). In the new system of units, we have: 1 unit of mass = 12.64\n kg, 1 unit of length = 53 m, 1 unit of time = 45 s. To find the value of x newtons, we need to determine the conversion factors between the new system and the standard SI units. The force (Newton) can be expressed as: x N = (m kg) * (l m) / (t^2 s^2). Substituting the given values into this equation, we have: x N = (m * 12.64\n kg) * (l * 53 m) / (t^2 * 45 s^2). Simplifying this expression will give us the value of x in newtons."
    },
    {
        "instruction": "A radio can tune over the frequency range of a portion of MW broadcast band: (263 kHz to 368 kHz). If its LC circuit has an effective inductance of 276 muH, what must be the range of its variable capacitor?",
        "input": "w1 = 2 * pi * f1\nC1 = 1 / ((w1 ** 2) * L)\nw2 = 2 * pi * (f1 + f2)\nC2 = 1 / ((w2 ** 2) * L)",
        "output": "6.78e-10 farad to 1.33e-09 farad"
    },
    {
        "instruction": "A series LCR circuit is connected to a variable frequency 230 V source with L = 30 H, C = 157 muF, R = 72 ohm. Determine the RMS potential drop across inductance?",
        "input": "RMS Potential Drop across Inductance = Current RMS * \u03c9_r * L",
        "output": "1.40e+03 volt"
    },
    {
        "instruction": "A copper wire has a length of 57 m and resistivity of 36 ohm-m. What is the cross-sectional area of this wire that makes its resistance 85 ohm?",
        "input": "R = 85 ohm, l = 57 m, rho = 36 ohm-m",
        "output": "The cross-sectional area of the wire required to achieve a resistance of 85 ohm is 24.1 m\u00b2. It is calculated by dividing the product of resistivity and length (2052) by the resistance."
    },
    {
        "instruction": "What is the potential energy of an object of mass 22 kg placed at a height 658 m?",
        "input": "PE = m * g * h",
        "output": "To calculate the potential energy, we use the formula PE = m * g * h, where PE is the potential energy, m is the mass (22 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height (658 m)., this is the final answer 141864.8"
    },
    {
        "instruction": "A sonar device on a submarine sends out a signal and receives an echo 958 s later. Find the speed of sound in that material if the distance of the object from the submarine is 4785 m ?\n",
        "input": "Distance = Speed * Time",
        "output": "10.0 m/s\nTo find the speed of sound in the material, we can use the equation: Speed = Distance / Time. In this case, the distance of the object from the submarine is 4785 meters and the time it takes for the echo to return is 958 seconds. Substituting these values into the equation, we can calculate the speed of sound in the material: Speed = 4785 m / 958 s. Calculating this expression will give us the speed of sound in the material."
    },
    {
        "instruction": "A car weighs 1083 kg. The distance between its front and back axles is 126 m. Its centre of gravity is 48 m behind the front axle. Determine the force exerted by the level ground on each front wheel and each back wheel.",
        "input": "Front Wheel Force = (m * g * (d - x)) / d\nBack Wheel Force = (m * g * x) / d",
        "output": "To calculate the force exerted on the front and back wheels, we use the following formulas:\n\nFront Wheel Force = (m * g * (d - x)) / d\nBack Wheel Force = (m * g * x) / d\n\nWhere,\n- m = Mass of the car\n- g = Acceleration due to gravity\n- d = Distance between front and back axles\n- x = Distance of the car's centre of gravity behind the front axle\n\nSubstituting the given values into the formulas, we find that the force exerted on each front wheel is approximately 6570.2 newtons and the force exerted on each back wheel is approximately 4043.2 newtons."
    },
    {
        "instruction": "An object is placed at 58 cm in front of a convex lens. Image is formed at a distance of 829 cm in front of it. Find the focal length of the lens.",
        "input": "Formula: 1/f = 1/v - 1/u for convex lens.",
        "output": "To find the focal length of the lens, we use the formula for convex lenses: 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for f. In this case, the focal length of the lens is 62.4 cm., this is the final The focal length of the lens is 62.4 cm."
    },
    {
        "instruction": "A pump on the ground floor of a building can pump up water to fill a tank of volume 50 m3 in 16 min. If the tank is 77 m above the ground, and the efficiency of the pump is 74%, how much electric power is consumed by the pump?\n",
        "input": "(100000*v*h*9.8)/(t*e)",
        "output": "To find the electricity in the pump: (100000*v*h*9.8)/(t*e), this is the final answer 53110.92watts\n"
    },
    {
        "instruction": "A satellite orbits the earth at a height of 1012 km above the surface. How much potential must be expended to rocket the satellite out of the planet's gravitational influence? Mass of the satellite = 200 kg; mass of the planet = 6e+24 kg; radius of the planet = 6400000.0 m.",
        "input": "-(g * m * M) / (r + h)",
        "output": "The gravitational potential required to rocket the satellite out of the planet's gravitational influence is approximately -1.25e+10 joules."
    },
    {
        "instruction": "Two amplifiers are connected one after the other in series(cascaded). The first amplifier has a voltage gain of 200 and the second has the voltage gain of 142. If the input signal is 0.058 volt, calculate the output ac signal.\n",
        "input": "V2 = V1*amp1*amp2",
        "output": "If the amplifiers are connected in series, the resultant amplification would be product of amplification factors of each of the amplifer, hence resultant output signal is 200*142*0.058 = 1.65e+03 volt\n"
    },
    {
        "instruction": "A wheel starting with an initial angular velocity of 24 rad/s is applied with a constant angular acceleration of 5 rad/s\u00b2. What is the time taken to reach an angular position of 977 rad?",
        "input": "time = (-(2 * initial_angular_velocity) + sqrt((4 * initial_angular_velocity^2) + (8 * angular_acceleration * angular_position))) / (2 * angular_acceleration)",
        "output": "To calculate the time, we use the following formula:\n\ntime = (-(2 * initial_angular_velocity) + sqrt((4 * initial_angular_velocity^2) + (8 * angular_acceleration * angular_position))) / (2 * angular_acceleration)\n\nSubstituting the given values into the formula, we find that the time is approximately 15.5 seconds."
    },
    {
        "instruction": "A convex lens produces 11 times magnified virtual image of an object placed at 83.07 cm in front of it. At what distance is the image formed from the lens?",
        "input": "Formula: v = n * u",
        "output": "To find the distance at which the image is formed from the lens, we use the formula v = n * u, where v is the distance of the image from the lens, n is the magnification factor, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for v. In this case, the image is formed at a distance of 913.8 cm from the lens., this is the final The image is formed at a distance of 913.8 cm from the lens."
    },
    {
        "instruction": "9 identical hollow cylindrical columns of mild steel support a big structure of mass 15360 kg. The inner and outer radii of each column are 28 cm and 48 cm respectively. Calculate the compressional strain of each column.",
        "input": "strain = F / (A * Y)",
        "output": "The compressional strain of each column is 1.8e-07."
    },
    {
        "instruction": "A train, standing at the outer signal of a railway station blows a whistle of frequency 205 Hz in still air. What is the frequency of the whistle for a platform observer of mass 97 kg when the train recedes from the platform with a speed of 52 ms-1\n",
        "input": "Apparent frequency = (speed of sound in air/speed of sound in air - speed of train)*original frequency",
        "output": "177.8 ms-1\nTo calculate the frequency of the whistle observed by a platform observer when a train passes by, we need to consider the Doppler effect due to the relative motion between the train and the observer. The Doppler effect accounts for the change in frequency observed when the source of sound and the observer are in relative motion."
    },
    {
        "instruction": "A meter stick of mass 75 g is balanced on a knife edge at its center. Where will the stick be balanced when a coin of mass 33 g is put at the 29 mark?",
        "input": "Balance Position = ((50 * m) + (m1 * t1)) / (m + m1)",
        "output": "The stick will be balanced at approximately 43.6 cm.\nBalance Position = ((50 * 75) + (33 * 29)) / (75 + 33)"
    },
    {
        "instruction": "Calculate root average velocity of a gas molecule having molar mass of 233 g/mol at 1592 degree C. (R = 8.31 J/molK)",
        "input": "math.sqrt((8 * r * t1 * 1000) / (math.pi * m))",
        "output": "411.5589273066658 m/s\n The formula used is: math.sqrt((8 * r * t1 * 1000) / (math.pi * m))"
    },
    {
        "instruction": "An Electric dipole with dipole moment 45 x 10^(-9) C-m is aligned at 73 degrees with the direction of a uniform electric field of magnitude 101 x 10^4 N C-1. Calculate the magnitude of torque acting on the dipole?\n",
        "input": "Torque = dipole moment * electric field * sin(theta)\n",
        "output": "The torque acting on an electric dipole in a uniform electric field can be calculated using the formula:\nSubstituting the given values:\nTorque = 45 x 10^(-9) C-m * 101 x 10^4 N C-1 * sin(73)\nTorque = 4.3e+03 newton-m\n"
    },
    {
        "instruction": "A solid sphere rolls down two different inclined planes of heights 12 and 7 and with angles of inclination of 47 and 50, on which it will reach the ground faster?",
        "input": "time = sqrt(height * (k + 1)) / sin(angle)",
        "output": "To compare the times, we use the following formula:\n\ntime = sqrt(height * (k + 1)) / sin(angle)\n\nSubstituting the given values into the formula, we find that:\n\nThe second plane takes less time to reach the ground."
    },
    {
        "instruction": "A helicopter of mass 682 kg rises with a vertical acceleration of 5 m/s^2. The crew and the passengers weigh 250 kg. Give the magnitude and direction of",
        "input": "force on the helicopter due to the surrounding air",
        "output": "13980 newton, vertically upwards\n\nThe force on the helicopter due to the surrounding air can be calculated based on the given mass (682 kg), weight of crew and passengers (250 kg), and acceleration (5 m/s^2)."
    },
    {
        "instruction": "In a process, 2650 J of heat is absorbed by the system and caused a change of 3178 J in internal energy of the system, what is the work done by the system ?\n",
        "input": "\u0394U = Q+W",
        "output": "from first law of thermodynamics, du = q + w => w = du - q => w = (3178) - (-2650) => w = 5828joule\n"
    },
    {
        "instruction": "The volume of 1636 g of a substance is 113 cm\u00b3. If the density of the liquid in which the substance is placed is 3 g/cm\u00b3, will the substance float or sink?",
        "input": "Density of Substance = 14.47787610619469 g/cm\u00b3, Density of Liquid = 3 g/cm\u00b3",
        "output": "The substance will sink."
    },
    {
        "instruction": "A particle starts from origin at t = 0 s with a velocity of (9) i + (-6) j ms-1 and moves in x-y plane with a constant acceleration of (9) i + (-7) j ms-2, then what is the speed of the particle at t = 4 s",
        "input": "v = sqrt(vx^2 + vy^2)",
        "output": "v = 56.4 ms-1"
    },
    {
        "instruction": "A small town with a demand of 900 kW of electric power at 220 V is situated 17 km away from an electric plant generating power at 440 V. The resistance of each of the two wires carrying power is 0.29 ohm per km. The town gets power from the line through 3740 - 220 V step down transformer at a sub-station in the town. Characterize the step-up transformer at the plant.",
        "input": "Voltage_Drop = I * resistance_drop * 2 * distance\nStep_up_transformer_rating = Bigger_voltage - Voltage_drop",
        "output": "rating is 440 volt -- 6.11e+03 volt"
    },
    {
        "instruction": "A pipe 74 cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a 135 Hz source? Will the same source be in resonance with the pipe if both ends are open? (speed of sound in air is 332 ms-1).\n",
        "input": "fundamental frequency = speed of sound in air/4*length of pipe",
        "output": "no resonance in first case, no resonance in second case\nResonance condition occurs when the frequency of external sources matches the natural frequency of the system."
    },
    {
        "instruction": "A bike starting with an initial velocity of 75 m/s travels on a straight road at a constant rate of 3 m/s\u00b2. What is the time taken to travel a distance of 497 m?",
        "input": "initial velocity (u) = 75 m/s, acceleration (a) = 3 m/s\u00b2, distance (s) = 497 m",
        "output": "distance (s) = initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)\u00b2\n497 = 75 * t + 0.5 * 3 * t\u00b2\n497 = 442.5 + 52.21500000000001\n497 = 497\n\n0.5 * 3 * t\u00b2 + 75 * t - 497 = 0\n1.5 * t\u00b2 + 75 * t - 497 = 0\n\nUsing quadratic formula, we get:\n\nt = (-75 \u00b1 \u221a(75\u00b2 - 4 * 1.5 * (-497))) / (2 * 1.5)\nt = (-75 \u00b1 \u221a(5625 - 2982)) / 3\nt = (-75 \u00b1 \u221a(8607)) / 3\nt = (-75 \u00b1 \u221a(8607)) / 3\nt = (-75 \u00b1 \u221a(8607)) / 3\nt = (-75 \u00b1 92.7739187487518) / 3\nt = 5.924639582917266 or -55.92463958291726\nt = 5.9 or 5.9\n\nSince time cannot be negative, t = 5.9"
    },
    {
        "instruction": "A hoop and a hollow cylinder roll down two different inclined planes of heights 7 and 6 and with angles of inclination of 27 and 52, which one reaches the bottom with more speed?",
        "input": "speed = height / (1 + k)",
        "output": "To compare the speeds, we use the following formula:\n\nspeed = height / (1 + k)\n\nSubstituting the given values into the formula, we find that:\n\nThe hoop reaches the bottom with more speed."
    },
    {
        "instruction": "A pipe 88 cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a 125 Hz source? Will the same source be in resonance with the pipe if both ends are open? (speed of sound in air is 348 ms-1).\n",
        "input": "fundamental frequency = speed of sound in air/4*length of pipe",
        "output": "no resonance in first case, no resonance in second case\nResonance condition occurs when the frequency of external sources matches the natural frequency of the system."
    },
    {
        "instruction": "What is the energy associated with a mass of 651.6 g ?\n",
        "input": "Energy = Mass*c^2",
        "output": "5.86e+16joule\nTo calculate the energy associated with a mass, we need to specify the type of energy we are referring to. There are various forms of energy, such as kinetic energy, potential energy, thermal energy, etc. If we assume you are referring to the energy associated with the mass in terms of its rest energy, we can use Einstein's mass-energy equivalence principle, given by the equation: E = m * c^2"
    },
    {
        "instruction": "A convex lens produces a real image of height 99 cm at a distance of 11 cm from it of a real object placed 41 cm in front of it. What is the height of the object?",
        "input": "Formula: ho = (hi * u) / v",
        "output": "To find the height of the object, we use the formula ho = (hi * u) / v, where ho is the height of the object, hi is the height of the image, u is the distance of the object from the lens, and v is the distance of the image from the lens. By substituting the given values into the formula, we can calculate ho. In this case, the height of the object is 369.0 cm., this is the final The height of the object is 369.0 cm."
    },
    {
        "instruction": "A concave mirror produces 44 times magnified real image of an object at a distance of 6847 cm from the mirror. At what distance is the object placed in front of the mirror?",
        "input": "Formula: u = v / n",
        "output": "To find the distance at which the object is placed in front of the mirror, we use the formula u = v / n, where u is the distance of the object from the mirror, v is the distance of the image from the mirror, and n is the magnification factor. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 155.6 cm in front of the mirror., this is the final The object is placed at a distance of 155.6 cm in front of the mirror."
    },
    {
        "instruction": "If a 1056 V battery is connected across an unknown resistor, there is 848 A in the circuit, find the value of resistance of the resistor?",
        "input": "Resistance = Voltage / Current",
        "output": "1.2 ohm\n\nThe resistance of the unknown resistor can be calculated using Ohm's law formula, where Resistance = Voltage / Current."
    },
    {
        "instruction": "The edge of a cube is 183 cm long. One face of the cube is firmly fixed to a vertical wall. A mass of 194 kg is then attached to the opposite face of the cube. The shear modulus of the material of the cube is 187 GPa. What is the vertical deflection of this face?",
        "input": "deflection = (mass * 9.8) / (Y * 10^9 * (edge_length * 10^-2))",
        "output": "To calculate the vertical deflection, we use the formula:\n\ndeflection = (mass * 9.8) / (Y * 10^9 * (edge_length * 10^-2))\n   = (194 kg * 9.8) / (187 * 10^9 GPa * (183 cm * 10^-2 m/cm))\n   = 5.6 nm."
    },
    {
        "instruction": "A short bar magnet of magnetic moment 8.34 J/T is placed in a uniform magnetic field of 4.7 T. If the magnet is free to rotate in the plane of the field, what is the potential energy of the magnet at a position making an angle of 133 degrees with the magnetic field?",
        "input": "-m * b * -0.68",
        "output": "The potential energy of the magnet at a position making an angle of -0.6819983600624984 degrees with the magnetic field can be calculated using the formula -m * b * cos(d), where 'm' is the magnetic moment of the bar magnet, 'b' is the magnetic field strength, and 'd' is the angle. Substituting the given values, we have -(8.34) * 4.7 * -0.68 = 2.67e+01 joule."
    },
    {
        "instruction": "A body weighs 117 N on the surface of the Earth. What is the gravitational force on it due to the Earth at a height equal to 31/51 the radius of the Earth?",
        "input": "Weight on the Surface (W) = 117 N, Height Ratio (n/d) = 31/51",
        "output": "The gravitational force on the body at a height equal to 31/51 the radius of the Earth is 72.8 newtons."
    },
    {
        "instruction": "A convex lens produces a real image at a distance of 922 cm from it of a real object placed 948 cm in front of it. What is the magnification of the lens?",
        "input": "Formula: m = v / u",
        "output": "To calculate the magnification of the lens, we use the formula m = v / u, where m is the magnification, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for m. In this case, the magnification of the lens is 1.0., this is the final The magnification of the lens is 1.0."
    },
    {
        "instruction": "An LC circuit contains a 134 mH inductor and a 171 muF capacitor with an initial charge of 18 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0. What is the natural frequency of the circuit.",
        "input": "Natural Frequency = 1 / (2 * pi * sqrt(Inductance * Capacitance))",
        "output": "3.32e+01 hertz"
    },
    {
        "instruction": "A girl sitting on a merry-go-round is moving in a counter-clockwise arc length of 844 m. If the angular displacement is 405 rad, how far is she from the center of the merry-go-round?",
        "input": "distance_from_center = arc_length / radius",
        "output": "To calculate the distance from the center, we use the following formula:\n\ndistance_from_center = arc_length / radius\n\nSubstituting the given values into the formula, we find that the distance from the center is approximately 2.1 m."
    },
    {
        "instruction": "What is the lowest total resistance that can be secured by combinations of three coils of resistance 42, 4, 62?",
        "input": "R_total = (R1 * R2 * R3) / (R1 * R2 + R2 * R3 + R3 * R1)",
        "output": "The lowest combination of resistances can be obtained by connecting them in parallel. The total resistance is calculated as (42 * 4 * 62) / (42 * 4 + 4 * 62 + 62 * 42) = 3.4 ohm.\n\nTo calculate the lowest combination of resistances, we connect them in parallel. The total resistance (R_total) is given by the formula (R1 * R2 * R3) / (R1 * R2 + R2 * R3 + R3 * R1), where R1, R2, and R3 are the individual resistances."
    },
    {
        "instruction": "A convex mirror produces a real image of height 43 cm at a distance of 69 cm from it of a real object having a height of 127 cm. At what distance is the object placed from the mirror?",
        "input": "Formula: m = v / u = hi / ho",
        "output": "To find the distance of the object from the mirror, we use the formula m = v / u = hi / ho, where m is the magnification, v is the distance of the image from the mirror, u is the distance of the object from the mirror, hi is the height of the image, and ho is the height of the object. By rearranging the formula, we can calculate u as u = (ho * v) / hi. By substituting the given values into the formula, we find that the object is placed at a distance of 203.8 cm from the mirror., this is the final The object is placed at a distance of 203.8 cm from the mirror."
    },
    {
        "instruction": "At t = 0, a wheel is rotating with an angular velocity of w rad/s at a constant angular acceleration of 13 rad/s\u00b2. It attains an angular velocity of 821 rad/s in t = 18 sec. What is the value of the initial angular velocity?",
        "input": "initial_angular_velocity = final_angular_velocity - (angular_acceleration * time)",
        "output": "To calculate the initial angular velocity, we use the following formula:\n\ninitial_angular_velocity = final_angular_velocity - (angular_acceleration * time)\n\nSubstituting the given values into the formula, we find that the initial angular velocity is approximately 587 rad/s."
    },
    {
        "instruction": "The coefficient of linear expansion of glycerine is 0.0004900000000000001 K^-1. What is the change in its volume 73 m^3 for a rise in temperature from 53 degree C to 390 degree C?",
        "input": "Change in volume = d1 * a * (t2 - t1)",
        "output": "To find the change in volume, we use the following formula:\n\nChange in volume = d1 * a * (t2 - t1)\n\nSubstituting the given values into the formula, we find that the change in volume is approximately 12.05 m^3."
    },
    {
        "instruction": "A convex lens produces 29 times diminished real image of an object at a distance of 26.64 cm from the lens. At what distance is the object placed in front of the lens?",
        "input": "Formula: u = v * n",
        "output": "To find the distance at which the object is placed in front of the lens, we use the formula u = v * n, where u is the distance of the object from the lens, v is the distance of the image from the lens, and n is the magnification factor. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 772.6 cm in front of the lens., this is the final The object is placed at a distance of 772.6 cm in front of the lens."
    },
    {
        "instruction": "A convex lens produces 52 times magnified virtual image of a 41.09 cm object placed in front of it. What is the height of the image formed by the lens?",
        "input": "Formula: hi = n * ho",
        "output": "To find the height of the image formed by the lens, we use the formula hi = n * ho, where hi is the height of the image, n is the magnification factor, and ho is the height of the object. By substituting the given values into the formula, we can solve for hi. In this case, the height of the image formed by the lens is 2136.7 cm., this is the final The height of the image formed by the lens is 2136.7 cm."
    },
    {
        "instruction": "An object is projected at an angle 28 from the ground, if the horizontal range of the object is 156 m, what is the initial velocity of it?",
        "input": "h = 156 m, theta = 28 degrees",
        "output": "42.9"
    },
    {
        "instruction": "A bat emits ultrasonic sound of frequency 112466 Hz in air. If this sound meets a water surface, what is the wavelength of the transmitted sound? (Speed of sound in air = 340 ms-1 and in water = 1486 ms-1)\n",
        "input": "wavelength of transmitted sound = speed of sound in water/frequency of the ultrasonic sound",
        "output": "1.32e-02 m\nGiven that the speed of sound in air is 340 m/s and the speed of sound in water is 1486 m/s, we can substitute these values into the formula to calculate the wavelength. For the sound emitted in air: \u03bb_air = (340 m/s) / 112466 Hz, For the sound reflected in water: \u03bb_water = (1486 m/s) / 112466 Hz"
    },
    {
        "instruction": "Two stars each of one solar mass 47000000000000000000000000000000 kg are approaching each other for a head-on collision. When they are at a distance 30000000000 km, their speeds are negligible. What is the speed with which they collide? The radius of each star is 820000 km. Assume the stars remain undistorted until they collide.",
        "input": "Speed = sqrt((-G*m/R) + (G*m/(2*r))) = sqrt(((-6.67 * 10^-11) * 47000000000000000000000000000000) / (30000000000000)) + ((6.67 * 10^-11) * 47000000000000000000000000000000) / (1640000000))",
        "output": "The speed with which the stars collide is approximately 1.38e+06 m/s."
    },
    {
        "instruction": "A body is dropped from a tower with an initial velocity of 2582 m/s and reaches the ground after 171 s. With what velocity does it reach the ground?",
        "input": "velocity = initial_velocity + (acceleration * time)",
        "output": "The body reaches the ground with a velocity of 4257.8 m/s."
    },
    {
        "instruction": "A small bulb is placed at the bottom of a tank containing liquid to a depth of 298 cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of the liquid is 2.07.",
        "input": "Formula: Area = \u03c0 * h\u00b2 * (k / (1 - k)), where h is the depth of the liquid in centimeters, k is the reciprocal of the refractive index of the liquid, and k = 1 / mu.",
        "output": "This is the answer 8.49 m\u00b2, formula used is : Formula: Area = \u03c0 * h\u00b2 * (k / (1 - k)), where h is the depth of the liquid in centimeters, k is the reciprocal of the refractive index of the liquid, and k = 1 / mu."
    },
    {
        "instruction": "A concave lens produces a real image at a distance of 9 cm from it of a real object having a height of 30 cm and placed 35 cm in front of it. What is the height of the image?",
        "input": "Formula: hi = (v * ho) / u",
        "output": "To find the height of the image, we use the formula hi = (v * ho) / u, where hi is the height of the image, ho is the height of the object, u is the distance of the object from the lens, and v is the distance of the image from the lens. By substituting the given values into the formula, we can solve for hi. In this case, the height of the image is 7.7 cm., this is the final The height of the image is 7.7 cm."
    },
    {
        "instruction": "A child stands at the centre of a turntable with his arms outstretched. The turntable is rotating with an angular speed of 177 rad/s. How many times is the kinetic energy of the rotation increased if he folds his hands back and thereby reduces his moment of inertia to 22/73 times the initial value?",
        "input": "Angular Speed = (n2 * w) / n1\nKinetic Energy Ratio = (n2^3) / (n1^3)",
        "output": "To calculate the angular speed and kinetic energy ratio, we use the following formulas:\n\nAngular Speed = (n2 * w) / n1\nKinetic Energy Ratio = (n2^3) / (n1^3)\n\nWhere,\n- n1 = Initial moment of inertia\n- n2 = Reduced moment of inertia\n- w = Initial angular speed\n\nSubstituting the given values into the formulas, we find that the kinetic energy of the rotation is increased by approximately 36.5 times."
    },
    {
        "instruction": "Find the focal length of a convex lens whose power is 25.51 D.",
        "input": "Formula: f = 1 / P",
        "output": "To find the focal length of a convex lens, we use the formula f = 1 / P, where f is the focal length and P is the power. By substituting the given value of P into the formula, we can solve for f. In this case, the focal length is 0.0 m., this is the final 0.0"
    },
    {
        "instruction": "A bike starting with an initial velocity of 97 m/s travels on a straight road at a constant rate of 2 m/s\u00b2. What is the time taken to travel a distance of 426 m?",
        "input": "initial velocity (u) = 97 m/s, acceleration (a) = 2 m/s\u00b2, distance (s) = 426 m",
        "output": "distance (s) = initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)\u00b2\n426 = 97 * t + 0.5 * 2 * t\u00b2\n426 = 407.40000000000003 + 17.64\n426 = 426\n\n0.5 * 2 * t\u00b2 + 97 * t - 426 = 0\n1.0 * t\u00b2 + 97 * t - 426 = 0\n\nUsing quadratic formula, we get:\n\nt = (-97 \u00b1 \u221a(97\u00b2 - 4 * 1.0 * (-426))) / (2 * 1.0)\nt = (-97 \u00b1 \u221a(9409 - 1704)) / 2\nt = (-97 \u00b1 \u221a(11113)) / 2\nt = (-97 \u00b1 \u221a(11113)) / 2\nt = (-97 \u00b1 \u221a(11113)) / 2\nt = (-97 \u00b1 105.41821474489122) / 2\nt = 4.209107372445608 or -101.2091073724456\nt = 4.2 or 4.2\n\nSince time cannot be negative, t = 4.2"
    },
    {
        "instruction": "What is the electric field at a point P at a distance of 227 m from the center of the spherical shell of radius 176 m and having 1.30e-06 C charge distributed uniformly on it?",
        "input": "Electric Field (E) = cal2(1.30e-06, 227, 176) N/C",
        "output": "2.27e-01 newton/coulomb\nThe electric field due to a uniformly charged spherical shell is given by the formula E = k * Q * r / (R^2), where k is the Coulomb's constant, Q is the charge on the shell, r is the distance from the center of the shell, and R is the radius of the shell. Plugging in the values, we get E = 2.27e-01 N/C."
    },
    {
        "instruction": "A concave lens produces 64 times diminished real image at a distance of 27.5 cm from the lens. At what distance is the object placed in front of the lens?",
        "input": "Formula: u = n * v",
        "output": "To find the distance at which the object is placed, we use the formula u = n * v, where u is the distance of the object from the lens, v is the distance of the image from the lens, and n is the magnification factor. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 1760.0 cm., this is the final The object is placed at a distance of 1760.0 cm."
    },
    {
        "instruction": "A person needs a lens of power -32198 dioptres for correcting his distant vision. What is the focal length of the lens required for correcting distant vision?\n",
        "input": "Power = 1/focal length (f)",
        "output": "we know that power(P)=1/f, hence f=1/P, f(in mm)=1000/P, hence f=0.03 mm\n"
    },
    {
        "instruction": "An object is placed at 63 cm in front of a concave mirror. Image is formed at a distance of 928 cm in front of it. Find the focal length of the mirror.",
        "input": "Formula: 1/f = 1/v + 1/u",
        "output": "To find the focal length of the mirror, we use the formula 1/f = 1/v + 1/u, where f is the focal length, v is the distance of the image, and u is the distance of the object. By substituting the given values into the formula, we can solve for f. In this case, the focal length of the mirror is 59.0 cm., this is the final 59.0"
    },
    {
        "instruction": "A train, standing in a station-yard, blows a whistle of frequency 429 Hz in still air. The wind starts blowing in the direction from the yard to the station with a speed of 35 ms-1. What is the wavelength for an observer standing on the station\u2019s platform? Compare it with situation when the air is still and the observer of mass 68 kg runs towards the yard at a speed of 35 ms-1?\n",
        "input": "Apparent frequency = (speed of sound in air/speed of sound in air - speed of train)*original frequency",
        "output": "case-1(wind) : 375/429 m, case-2(observer) : 340/429 m\nTo calculate the frequency heard by an observer standing on the station's platform when the wind is blowing, we need to consider the Doppler effect due to the relative motion between the source of sound and the observer. Given that the train blows a whistle of frequency 429 Hz in still air and the wind is blowing in the direction from the yard to the station with a speed of 35 m/s, we can determine the observed frequency for the platform observer.The formula to calculate the observed frequency is: f' = f * (v_sound + v_wind) / (v_sound), where f' is the observed frequency, f is the emitted frequency, v_sound is the speed of sound in still air, and v_wind is the velocity of the wind."
    },
    {
        "instruction": "A small bulb is placed at the bottom of a tank containing liquid to a depth of 176 cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of the liquid is 1.4.",
        "input": "Formula: Area = \u03c0 * h\u00b2 * (k / (1 - k)), where h is the depth of the liquid in centimeters, k is the reciprocal of the refractive index of the liquid, and k = 1 / mu.",
        "output": "This is the answer 10.14 m\u00b2, formula used is : Formula: Area = \u03c0 * h\u00b2 * (k / (1 - k)), where h is the depth of the liquid in centimeters, k is the reciprocal of the refractive index of the liquid, and k = 1 / mu."
    },
    {
        "instruction": "A concave mirror produces 54 times magnified virtual image of an object at a distance of 2305 cm from the mirror. At what distance is the object placed in front of the mirror?",
        "input": "Formula: u = v * n",
        "output": "To find the distance at which the object is placed in front of the mirror, we use the formula u = v * n, where u is the distance of the object from the mirror, v is the distance of the image from the mirror, and n is the magnification factor. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 124470 cm in front of the mirror., this is the final The object is placed at a distance of 124470 cm in front of the mirror."
    },
    {
        "instruction": "A child stands at the centre of a turntable with his arms outstretched. The turntable is rotating with an angular speed of 17 rad/s. How many times is the kinetic energy of the rotation increased if he folds his hands back and thereby reduces his moment of inertia to 95/178 times the initial value?",
        "input": "Angular Speed = (n2 * w) / n1\nKinetic Energy Ratio = (n2^3) / (n1^3)",
        "output": "To calculate the angular speed and kinetic energy ratio, we use the following formulas:\n\nAngular Speed = (n2 * w) / n1\nKinetic Energy Ratio = (n2^3) / (n1^3)\n\nWhere,\n- n1 = Initial moment of inertia\n- n2 = Reduced moment of inertia\n- w = Initial angular speed\n\nSubstituting the given values into the formulas, we find that the kinetic energy of the rotation is increased by approximately 6.6 times."
    },
    {
        "instruction": "A short bar magnet of magnetic moment 8.13 J/T is placed in a uniform magnetic field of 2.2 T. If the magnet is free to rotate in the plane of the field, what is the potential energy of the magnet at stable position?",
        "input": "-m * b",
        "output": "The potential energy of the magnet at a stable position can be calculated using the formula -m * b, where 'm' is the magnetic moment of the bar magnet and 'b' is the magnetic field strength. Substituting the given values, we have -(8.13) * 2.2 = -1.79e+01 joule."
    },
    {
        "instruction": "On an unknown scale, the temperature of the melting point and boiling point of water is -82 degrees and 159 degrees respectively. If the temperature on the Celsius scale is 115 degrees Celsius, what is the temperature shown on that scale?",
        "input": "Temperature on the unknown scale = (((t2 - t1) * (t - ta)) / (tb - ta)) + t1",
        "output": "To find the temperature on the unknown scale, we use the following formula:\n\nTemperature on the unknown scale = (((t2 - t1) * (t - ta)) / (tb - ta)) + t1\n\nSubstituting the given values into the formula, we find that the temperature on the unknown scale is approximately 195.1."
    },
    {
        "instruction": "What is the electric field at a point P on the surface of the spherical shell of radius 125 m and having -5.40e-07 C charge distributed uniformly on it?",
        "input": "Electric Field (E) = cal3(-5.40e-07, 125) N/C",
        "output": "-3.11e-01 newton/coulomb\nThe electric field on the surface of a uniformly charged spherical shell is given by the formula E = k * Q / (R^2), where k is the Coulomb's constant, Q is the charge on the shell, and R is the radius of the shell. Plugging in the values, we get E = -3.11e-01 N/C."
    },
    {
        "instruction": "A wheel reaches an angular position of 2984 rad when applied with a constant angular acceleration of 86 rad/s\u00b2 for 8 seconds. What is its initial angular velocity?",
        "input": "initial_angular_velocity = (angular_position - (0.5 * angular_acceleration * time^2)) / time",
        "output": "To calculate the initial angular velocity, we use the following formula:\n\ninitial_angular_velocity = (angular_position - (0.5 * angular_acceleration * time^2)) / time\n\nSubstituting the given values into the formula, we find that the initial angular velocity is approximately 29.0 rad/s."
    },
    {
        "instruction": "An Electric bulb of resistance 31 ohm produces heat at 66 W for 1035 s. Calculate the potential difference maintained at service mains?",
        "input": "V = sqrt(P * R)",
        "output": "45.2 volt\n\nThe potential difference maintained at service mains can be calculated using the formula: V = sqrt(P * R), where P is the power and R is the resistance."
    },
    {
        "instruction": "A truck starts from rest and accelerates uniformly at 1 ms-2. At t = 33 s, a stone is dropped by a person standing on the top of the truck (23 m high from the ground). What are the (a) velocity, and (b) acceleration of the stone at t = 48 s? (Neglect air resistance.)",
        "input": "A truck starts from rest and accelerates uniformly at 1 ms-2. At t = 33 s, a stone is dropped by a person standing on the top of the truck (23 m high from the ground). What are the (a) velocity, and (b) acceleration of the stone at t = 48 s? (Neglect air resistance.)",
        "output": "Velocity is 153.6 ms-1, at an angle of 78 degrees with horizontal. Acceleration is g (10 ms-2) downwards."
    },
    {
        "instruction": "A wheel starting with an initial angular velocity of 94 rad/s accelerates with a constant angular acceleration of 63 rad/s\u00b2. If it reaches an angular position of 22 rad, then what is its final velocity?",
        "input": "final_angular_velocity = sqrt(initial_angular_velocity^2 + (2 * angular_acceleration * angular_position))",
        "output": "To calculate the final angular velocity, we use the following formula:\n\nfinal_angular_velocity = sqrt(initial_angular_velocity^2 + (2 * angular_acceleration * angular_position))\n\nSubstituting the given values into the formula, we find that the final angular velocity is approximately 107.7 rad/s."
    },
    {
        "instruction": "A force of 215 N acts on an object. The displacement is 848 m in the direction of the force, then what is the work done by this force?",
        "input": "W = F * s",
        "output": "Using the formula: W = F * s, the final answer is: {'answer': '182320 J', 'explanation': 'To calculate the work done by a force, we use the formula W = F * s, where W is the work done, F is the force (215 N), and s is the displacement (848 m).'}"
    },
    {
        "instruction": "A hole is drilled in a steel sheet. The diameter of the hole is 41 cm at 39 degree C. What is the change in the diameter of the hole when the sheet is heated to 194 degree C? Coefficient of linear expansion of steel = 1.2 x 10-5K-1.",
        "input": "Change in diameter = initial diameter * sqrt(1 + (coefficient of linear expansion * initial diameter * (final temperature - initial temperature))) - initial diameter",
        "output": "To calculate the change in diameter, we use the following formula:\n\nChange in diameter = initial diameter * sqrt(1 + (coefficient of linear expansion * initial diameter * (final temperature - initial temperature))) - initial diameter\n\nSubstituting the given values into the formula, we find that the change in diameter is approximately 1.535 cm."
    },
    {
        "instruction": "The coefficient of volume expansion of copper is 5.1e-05 K^-1. What is the change in its volume 63 m^3 for a rise in temperature from 14 degree C to 318 degree C?",
        "input": "Change in volume = d1 * a * (t2 - t1)",
        "output": "To find the change in volume, we use the following formula:\n\nChange in volume = d1 * a * (t2 - t1)\n\nSubstituting the given values into the formula, we find that the change in volume is approximately 0.98 m^3."
    },
    {
        "instruction": "Toricelli's barometer used mercury. If someone duplicated it using some liquid of density 1061 kg/m3. Determine the height of the liquid column for normal atmospheric pressure (density of material of barometer is 2000 kg/m3).",
        "input": "(1.01 * (10 ** 5)) / (1061 * 9.8)",
        "output": "9.713593260112715"
    },
    {
        "instruction": "A circular coil of wire consisting of 176 turns, each of radius 899 cm placed in a horizontal plane carries a current of 13 A in clockwise direction. What is the magnitude and direction of the magnetic field B at the center of the coil?",
        "input": "B = (mu * n * i) / (2 * r)",
        "output": "To calculate the magnetic field B at the center of the coil, we use the following formula:\n\nB = (mu * n * i) / (2 * r)\n\nWhere,\n- B = Magnetic field at the center of the coil\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- n = Number of turns in the coil\n- i = Current flowing through the coil\n- r = Radius of the coil\n\nSubstituting the given values into the formula, we find that the magnitude of the magnetic field B is approximately 1.60e-04 tesla vertically downwards."
    },
    {
        "instruction": "Two stars each of one solar mass 89000000000000000000000000000000 kg are approaching each other for a head-on collision. When they are at a distance 14000000000 km, their speeds are negligible. What is the speed with which they collide? The radius of each star is 600000 km. Assume the stars remain undistorted until they collide.",
        "input": "Speed = sqrt((-G*m/R) + (G*m/(2*r))) = sqrt(((-6.67 * 10^-11) * 89000000000000000000000000000000) / (14000000000000)) + ((6.67 * 10^-11) * 89000000000000000000000000000000) / (1200000000))",
        "output": "The speed with which the stars collide is approximately 2.22e+06 m/s."
    },
    {
        "instruction": "A hoop of mass 927 kg has a radius of 86 m. What is the moment of inertia with respect to its diameter?",
        "input": "Moment of Inertia = (Constant) * mass * radius^2",
        "output": "The moment of inertia with respect to its diameter is approximately 3428046.0 kgm^2.\n\nMoment of Inertia = (Constant) * mass * radius^2\n\nConstant = 0.5\nmass = 927 kg\nradius = 86 m"
    },
    {
        "instruction": "Suppose we employ a system of units in which the unit of mass equals 45 kg, the unit of length equals 50 m, the unit of time is 60 s, if the value of x joule is equal to 7 units in new system, find x?\n",
        "input": "x J = (m kg) * (l m^2) / (t^2 s^2)",
        "output": "218.75\nTo find the value of x joules in the given system of units, we need to consider the relationships between the units of mass (kg), length (m), time (s), and energy (Joule). In the new system of units, we have: 1 unit of mass = 218.75\n kg, 1 unit of length = 50 m, 1 unit of time = 60 s. To find the value of x joules, we need to determine the conversion factors between the new system and the standard SI units. The energy (Joule) can be expressed as: x J = (m kg) * (l m^2) / (t^2 s^2). Substituting the given values into this equation, we have: x J = (m * 218.75\n kg) * (l * 50 m^2) / (t^2 * 60 s^2). Simplifying this expression will give us the value of x in joules."
    },
    {
        "instruction": "At t = 0, a wheel is rotating with an angular velocity of w rad/s at a constant angular acceleration of 23 rad/s\u00b2. It attains an angular velocity of 657 rad/s in t = 30 sec. What is the value of the initial angular velocity?",
        "input": "initial_angular_velocity = final_angular_velocity - (angular_acceleration * time)",
        "output": "To calculate the initial angular velocity, we use the following formula:\n\ninitial_angular_velocity = final_angular_velocity - (angular_acceleration * time)\n\nSubstituting the given values into the formula, we find that the initial angular velocity is approximately -33 rad/s."
    },
    {
        "instruction": "An object is projected with an initial velocity of 272 m/s at an angle 53 from the ground, what is the horizontal range of the object?",
        "input": "v = 272 m/s, theta = 53 degrees",
        "output": "7256.9"
    },
    {
        "instruction": "The coefficient of linear expansion of copper is 5.1e-05 K^-1. What is the change in its volume 99 m^3 for a rise in temperature from 96 degree C to 319 degree C?",
        "input": "Change in volume = d1 * a * (t2 - t1)",
        "output": "To find the change in volume, we use the following formula:\n\nChange in volume = d1 * a * (t2 - t1)\n\nSubstituting the given values into the formula, we find that the change in volume is approximately 1.13 m^3."
    },
    {
        "instruction": "Two charges q1 of -134 x 10^(-8)C and q2 of 104 x 10^(-8) are located 25 cm apart. At what point(s) on the line joining the two charges is the electric potential zero (take potential at infinity as zero)?",
        "input": "Charge q1 : -134 x 10^(-8) C , Charge q2: 104 x 10^(-8) C, Distance (d) : 25 cm",
        "output": "1.41e+01 cm from q1 between q1 and q2, 1.12e+02 cm from q1 to the right of both charges\n\nExplanation: To find the point(s) on the line where the electric potential is zero, we can use the formula r = (q1 * d) / (q1 - q2), where r is the distance from q1. If the magnitudes of q1 and q2 are not equal, there will be a second point given by r = (q1 * d) / (q1 + q2). Plugging in the values, we get the point(s) as follows: 1.41e+01 cm from q1 between q1 and q2, 1.12e+02 cm from q1 to the right of both charges\n"
    },
    {
        "instruction": "Two absolute scales A and B have triple points of water defined to be 16 A and -179 B. What is the relation between TA and TB?",
        "input": "Relation between TA and TB = TA / TB",
        "output": "To find the relation between TA and TB, we divide the temperature on scale A (TA) by the temperature on scale B (TB). Therefore, the relation is given by:\n\nRelation between TA and TB = TA / TB\n\nSubstituting the given values, we find that the relation is approximately -0.09."
    },
    {
        "instruction": "A person is listening to a tone of 867034 Hz sitting at a distance of 17 m from the source of the sound. What is the time interval between successive compressions from the source?\n",
        "input": "Time interval = Distance / Speed",
        "output": "1.2 microseconds\nTo calculate the time interval between successive compressions from the source, we need to consider the speed of sound in the medium. The speed of sound in air at room temperature is approximately 343 meters per second. The time interval between successive compressions (or any two consecutive points with maximum compression) can be calculated using the formula: Time interval = Distance / Speed. In this case, the distance from the source of the sound is 17 meters and the speed of sound is approximately 343 m/s. Substituting these values into the formula, we can calculate the time interval between successive compressions: Time interval = 17 m / 343 m/s. Calculating this expression will give us the time interval between successive compressions from the source."
    },
    {
        "instruction": "Two gold pieces of masses are 8899000 g and 597 g respectively. What is the difference of the masses of the pieces to correct significant figures?\n",
        "input": "",
        "output": "8.89e+06\n"
    },
    {
        "instruction": "A capacitor made of two circular plates of radius 64 cm, and separated by 153 cm. The capacitor is being charged by an external source. The charging current is constant and equal to 150 mA. Calculate the capacitance between the plates?",
        "input": "r = 64 cm, s = 153 cm",
        "output": "7.44e-12 farad\n\nThe capacitance of a capacitor can be calculated using the formula: C = (\u03b5\u03c0r\u00b2) / s, where \u03b5 is the permittivity of free space, r is the radius of the plates, and s is the separation between the plates."
    },
    {
        "instruction": "In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are 55 ms-1 and 47 ms-1. What is the lift on the wing if its area is 4700 cm2? (Take the density of air to be 1.3 kgm-3)",
        "input": "0.5 * 1.3 * (55**2 - 47**2) * (4700 / 10000)",
        "output": "The lift on the wing is 249.28799999999998 newton."
    },
    {
        "instruction": "Two charges q1 of 141 x 10^(-8)C and q2 of -33 x 10^(-8) are located 153 cm apart. At what point(s) on the line joining the two charges is the electric potential zero (take potential at infinity as zero)?",
        "input": "Charge q1 : 141 x 10^(-8) C , Charge q2: -33 x 10^(-8) C, Distance (d) : 153 cm",
        "output": "1.24e+02 cm from q1 between q1 and q2, 2.00e+02 cm from q1 to the right of both charges\n\nExplanation: To find the point(s) on the line where the electric potential is zero, we can use the formula r = (q1 * d) / (q1 - q2), where r is the distance from q1. If the magnitudes of q1 and q2 are not equal, there will be a second point given by r = (q1 * d) / (q1 + q2). Plugging in the values, we get the point(s) as follows: 1.24e+02 cm from q1 between q1 and q2, 2.00e+02 cm from q1 to the right of both charges\n"
    },
    {
        "instruction": "A force is applied on a body of mass 915 kg placed on a smooth surface resulting in acceleration of 203 m/s^2, then what is the force applied?",
        "input": "F = m * a",
        "output": "185745\nTo calculate the force, we use the formula F = m * a, where F is the force, m is the mass (915 kg), and a is the acceleration (203 m/s^2)."
    },
    {
        "instruction": "Two bodies A, B of masses 107 kg and 60 kg respectively kept on a smooth, horizontal surface are tied to the ends of a tight string. A horizontal force F = 355 N is applied to B along the direction of the string. What is the acceleration and tension in the string?",
        "input": "",
        "output": "The acceleration is 2.1 m/s^2, and the tension is 227.5 N."
    },
    {
        "instruction": "A short bar magnet of magnetic moment 7.48 J/T is placed in a uniform magnetic field of 19.85 T. If the magnet is free to rotate in the plane of the field, what is the potential energy of the magnet at unstable position?",
        "input": "m * b",
        "output": "The potential energy of the magnet at an unstable position can be calculated using the formula m * b, where 'm' is the magnetic moment of the bar magnet and 'b' is the magnetic field strength. Substituting the given values, we have 7.48 * 19.85 = 1.48e+02 joule."
    },
    {
        "instruction": "A steady current of 47 A flows through a conductor, then calculate the number of electrons through any cross section of the conductor in 404 s?",
        "input": "n = (I * t) / e",
        "output": "1.18675e+23\n\nThe number of electrons through any cross section of the conductor can be calculated using the formula: n = (I * t) / e, where I is the current, t is the time, and e is the charge of an electron."
    },
    {
        "instruction": "In a chamber, a uniform magnetic field of 0.0103 T is maintained. An electron is shot into the field with a speed of 90000000 m/s, making an angle of 11 degrees with the field. Determine the radius of the circular path of the electron.",
        "input": "Radius = (m * v) / (b * e * sin(d))",
        "output": "To calculate the radius of the circular path, we use the following formula:\n\nRadius = (m * v) / (b * e * sin(d))\n\nWhere,\n- m = Mass of the electron\n- v = Speed of the electron\n- b = Magnetic field\n- e = Charge of the electron\n- d = Angle between the velocity vector and the magnetic field vector\n\nWe substitute the given values into the formula and evaluate it to find that the radius of the circular path of the electron is approximately 2.60e-01 m."
    },
    {
        "instruction": "What is the gravitational potential at a point P at a distance of 85 m from the center of the uniform solid sphere of radius 185 m and mass 330 kg?",
        "input": "Gravitational Potential (V) = cal1(330, 85, 185) joule/kg",
        "output": "The gravitational potential at a point P at a distance of 85 m from the center of the uniform solid sphere of radius 185 m and mass 330 kg is given by the formula V = (-G * m * (3 * R^2 - r^2)) / (2 * R^3), where G is the gravitational constant, m is the mass, r is the distance, and R is the radius. Plugging in the values, we get V = -1.66e-10 joule/kg."
    },
    {
        "instruction": "A concave mirror produces 48 times magnified real image of height 1543 cm of an object placed in front of it. What is the height of the object taken?",
        "input": "Formula: ho = hi / n",
        "output": "To find the height of the object taken, we use the formula ho = hi / n, where ho is the height of the object, hi is the height of the image, and n is the magnification factor. By substituting the given values into the formula, we can solve for ho. In this case, the height of the object taken is 32.1 cm., this is the final The height of the object taken is 32.1 cm."
    },
    {
        "instruction": "What is the magnitude of the magnetic force per unit length on a wire carrying a current of 88 A and making an angle of 54 degrees with the direction of a uniform magnetic field of 93 tesla?",
        "input": "Force per unit length = b * i * sin(d)",
        "output": "To calculate the magnitude of the magnetic force, we use the following formula:\n\nForce per unit length = b * i * sin(d)\n\nSubstituting the given values:\n- b = 93 tesla\n- i = 88 A\n- d = 54 degrees\n\nAfter evaluating the formula, we find that the magnetic force per unit length is approximately 6621.0 newtons per meter."
    },
    {
        "instruction": "What is the excess pressure inside a bubble of soap solution of radius 3 mm, given that the surface tension of soap solution at the temperature 280 K is 162 x 10-3 Nm-1? If an air bubble of the same dimension was formed at a depth of 80 cm inside a container containing the soap solution (of relative density 2.5), what would be the pressure inside the bubble?",
        "input": "(4 * 162) / 3",
        "output": "The excess pressure inside the soap bubble is 216.0 Pascal. The pressure inside the air bubble floating up is 1.03e+05 Pascal."
    },
    {
        "instruction": "What is the gravitational potential at a point P at a distance of 481 m from the center of the spherical shell of radius 548 m and mass 495 kg?",
        "input": "Gravitational Potential (V) = cal1(495, 481, 548) joule/kg",
        "output": "The gravitational potential at a point P at a distance of 481 m from the center of the spherical shell of radius 548 m and mass 495 kg is given by the formula V = (-G * m) / R, where G is the gravitational constant, m is the mass, and R is the distance. Plugging in the values, we get V = -6.02e-11 joule/kg."
    },
    {
        "instruction": "A copper block of mass 1430 g is heated in a furnace to a temperature of 777 degree C and then placed on a large ice block. What is the maximum amount of ice that can melt? Specific heat of copper is 0.39 Jg-1\u00b0C-1. Heat of fusion of water = 335 Jg-1.",
        "input": "Maximum amount of ice melted = (mass of block * temperature change * specific heat) / heat of fusion of water",
        "output": "To calculate the maximum amount of ice melted, we use the following formula:\n\nMaximum amount of ice melted = (mass of block * temperature change * specific heat) / heat of fusion of water\n\nSubstituting the given values into the formula, we find that the maximum amount of ice that can melt is approximately 1293.5 g."
    },
    {
        "instruction": "Calculate the energy of each of the photons which have wavelength of 279555 nm.\n",
        "input": "Energy = h*c/wavelength",
        "output": "7.08e-22joules\nTo calculate the energy of a photon, you can use the formula: E = h * c/lambda, where E is the energy of the photon, h is the Planck constant (approximately 6.626 x 10^-34 J\u00b7s), c is the speed of light and lambda is the wavelength of the light."
    },
    {
        "instruction": "What is the pressure inside a drop of liquid of radius 16 mm at room temperature? Surface tension of liquid at that temperature (315 K) is 927 x 10^(-3) Nm^(-1). Also give the excess pressure inside the drop.",
        "input": "excess pressure = (2 * surface tension) / radius, total pressure = 1.01 * (10 ** 5) + excess pressure",
        "output": "The excess pressure inside the drop is 115.88 pascal. The total pressure inside the drop is 1.01e+05 pascal."
    },
    {
        "instruction": "Suppose we employ a system of units in which the unit of mass equals 19 kg, the unit of length equals 40 m, the unit of time is 50 s, then value of 17 newton in new system\n",
        "input": "17 N = (m kg) * (l m) / (t^2 s^2)",
        "output": "55.92\nTo find the value of 17 newtons in the given system of units, we need to consider the relationships between the units of mass (kg), length (m), time (s), and force (Newton). In the new system of units, we have: 1 unit of mass = 55.92\n kg, 1 unit of length = 40 m, 1 unit of time = 50 s. To find the value of 17 newtons, we need to determine the conversion factors between the new system and the standard SI units. The force (Newton) can be expressed as: 17 N = (m kg) * (l m) / (t^2 s^2). Substituting the given values into this equation, we have: 17 N = (m * 55.92\n kg) * (l * 40 m) / (t^2 * 50 s^2). Simplifying this expression will give us the value of 17 newtons in the new system of units."
    },
    {
        "instruction": "Two circular coils X and Y of radii 18 cm and 16 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil A has 11 turns and carries a current of 31 A, Coil B has 13 turns and carries a current of 25 A. The sense of current in X is anti-clockwise direction and in Y is clockwise direction. From an observer looking at the coils facing west, give the magnitude and direction of the net magnetic field due to the coils at the center.",
        "input": "Net magnetic field = |b1 - b2|",
        "output": "To calculate the net magnetic field, we use the following formula:\n\nNet magnetic field = |b1 - b2|\n\nWhere,\n- b1 = Magnetic field due to coil X\n- b2 = Magnetic field due to coil Y\n\nWe calculate the magnetic field for each coil using the formula:\n- Magnetic field due to coil X = (mu * n1 * i1) / (2 * r1)\n- Magnetic field due to coil Y = (mu * n2 * i2) / (2 * r2)\n\nSubstituting the given values and evaluating the formula, we find that the magnitude of the net magnetic field is approximately 8.60e-05 tesla and towards west."
    },
    {
        "instruction": "A bike starting with an initial velocity of 79 m/s travels a distance of 520 m on a straight road for 3 s. What is the acceleration of the bike?",
        "input": "initial velocity (u) = 79 m/s, distance (s) = 520 m, time (t) = 3 s",
        "output": "distance (s) = initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)\u00b2\n520 = 79 * 3 + 0.5 * a * 3\u00b2\n520 = 237 + 0.5 * a * 3\u00b2\n520 = 237 + 283.04999999999995\n520 = 520\n\n520 - 237 = 283.04999999999995\n62.9 = 2 * (520 - 237) / 3\u00b2\n62.9 = 62.9"
    },
    {
        "instruction": "A radio can tune in to any station in the 782 kHz to 3101 kHz band. What is the corresponding wavelength band?",
        "input": "f1 = 782 kHz, f2 = 2319 kHz",
        "output": "96.74 m to 383.63 m\n\nThe corresponding wavelength band can be calculated by dividing the speed of light by the frequency range."
    },
    {
        "instruction": "A 9984 N force is applied on a body of mass 101 kg placed on a smooth surface, then what is the resulting acceleration obtained?",
        "input": "a = F / m",
        "output": "98.9\nTo calculate the acceleration, we use the formula a = F / m, where a is the acceleration, F is the force (9984 N), and m is the mass (101 kg)."
    },
    {
        "instruction": "A sound wave travels at a speed of 174380.0 m/s, if it's wavelength is 20 m, will the sound wave be audible ? \n",
        "input": "frequency = wave speed / wavelength",
        "output": "audible\nWhether a sound wave is audible or not depends on its frequency, not its wavelength. Audible sound waves have frequencies within the range of human hearing, which is typically between 20 Hz and 20,000 Hz. To determine if a sound wave is audible, we need to calculate its frequency using the wave speed and wavelength. The formula to calculate the frequency of a sound wave is: f = v / \u03bb, where f is the frequency, v is the wave speed, and \u03bb is the wavelength. Substituting the given values into the formula, we can calculate the frequency of the sound wave: f = 174380.0 m/s / 20 m. Now, we can compare the calculated frequency to the audible frequency range (20 Hz to 20,000 Hz) to determine if the sound wave is audible or not."
    },
    {
        "instruction": "What is the gravitational potential at a point P on the surface of the uniform solid sphere of radius 290 m and mass 467 kg?",
        "input": "Gravitational Potential (V) = cal3(467, 290) joule/kg",
        "output": "The gravitational potential at a point P on the surface of the uniform solid sphere of radius 290 m and mass 467 kg is given by the formula V = (-G * m) / r, where G is the gravitational constant, m is the mass, and r is the distance. Plugging in the values, we get V = -1.07e-10 joule/kg."
    },
    {
        "instruction": "A small bulb is placed at the bottom of a tank containing liquid to a depth of 206 cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of the liquid is 2.41.",
        "input": "Formula: Area = \u03c0 * h\u00b2 * (k / (1 - k)), where h is the depth of the liquid in centimeters, k is the reciprocal of the refractive index of the liquid, and k = 1 / mu.",
        "output": "This is the answer 2.77 m\u00b2, formula used is : Formula: Area = \u03c0 * h\u00b2 * (k / (1 - k)), where h is the depth of the liquid in centimeters, k is the reciprocal of the refractive index of the liquid, and k = 1 / mu."
    },
    {
        "instruction": "If a 583 V battery is connected across a resistance of 169 ohm, then find the current in the circuit?",
        "input": "Current = Voltage / Resistance",
        "output": "3.4 ampere\n\nThe current in the circuit can be calculated using Ohm's law formula, where Current = Voltage / Resistance."
    },
    {
        "instruction": "A TV antenna is 32293 cm tall. How much service area can it cover if the receiving antenna is at ground level?",
        "input": "Service_area = pi * 2 * 6.4 * 10000 * l",
        "output": "1.30e+10 m2"
    },
    {
        "instruction": "What is the lowest total resistance that can be secured by combinations of three coils of resistance 76, 74, 87?",
        "input": "R_total = (R1 * R2 * R3) / (R1 * R2 + R2 * R3 + R3 * R1)",
        "output": "The lowest combination of resistances can be obtained by connecting them in parallel. The total resistance is calculated as (76 * 74 * 87) / (76 * 74 + 74 * 87 + 87 * 76) = 26.2 ohm.\n\nTo calculate the lowest combination of resistances, we connect them in parallel. The total resistance (R_total) is given by the formula (R1 * R2 * R3) / (R1 * R2 + R2 * R3 + R3 * R1), where R1, R2, and R3 are the individual resistances."
    },
    {
        "instruction": "What is the magnitude and direction of (657) i + (478) j?",
        "input": "magnitude = sqrt(657^2 + 478^2), direction = atan(478/657) * (180 / pi)",
        "output": "The magnitude is 812.5 and the direction is 36 degrees with the positive x-axis."
    },
    {
        "instruction": "What is the phase of the SHM with equation (-188)*sin(27wt) + (-72)*cos(27wt)? (i.e., if written as Asin(bwt+theta), then what is the value of theta)\n",
        "input": "Equation: (-188)*sin(27wt) + (-72)*cos(27wt)",
        "output": "Using this formula: Equation: (-188)*sin(27wt) + (-72)*cos(27wt), this is the final answer derived: 21 degrees\n"
    },
    {
        "instruction": "A concave mirror produces a virtual image of height 1309 cm of a real object of height 762 cm placed in front of it. What is the magnification of the mirror?",
        "input": "Formula: m = hi / ho",
        "output": "To find the magnification of the mirror, we use the formula m = hi / ho, where m is the magnification, hi is the height of the virtual image, and ho is the height of the real object. By substituting the given values into the formula, we can solve for m. In this case, the magnification of the mirror is 1.7., this is the final The magnification of the mirror is 1.7."
    },
    {
        "instruction": "If a diatomic gas of 4 moles at 31 pas is isothermally changed to pressure 24 pas at 60 K, then what is the work done.\n",
        "input": "Work Done = n*R*T*ln(P1/P2)",
        "output": "-510.4 joules\nTo calculate the work done during an isothermal expansion of a diatomic gas, we can use the following equation: Work done = n * R * T * ln(P1/P2), where n is the number of moles of the gas, R is the ideal gas constant (approximately 8.314 J/(mol\u00b7K)), T is the temperature in Kelvin, P1 is the initial pressure, and P2 is the final pressure."
    },
    {
        "instruction": "A bullet of mass 81 kg and horizontal speed 61 m/s strikes a block of wood of mass 61 kg and instantly comes to rest with respect to the block. Estimate the amount of heat produced in the block.",
        "input": "Heat = K1 - K2",
        "output": "To calculate the amount of heat produced, we use the formula Heat = K1 - K2, where K1 is the initial kinetic energy of the bullet and K2 is the final kinetic energy of the system after the collision., this is the final answer -2841173.8"
    },
    {
        "instruction": "What is the largest average velocity of blood flow in an artery of radius 1024 micrometer and length 388 mm if flow must remain laminar? What is the corresponding flow rate?",
        "input": "(2000 * 2.084) / (1.06 * 2 * 1024)",
        "output": "The largest average velocity of blood flow is 1.92 m/s. The corresponding flow rate is 6.32e-06 m^3/s."
    },
    {
        "instruction": "A SONAR system fixed in a submarine operates at a frequency 58920 Hz. An enemy submarine moves towards the SONAR with a speed of 513 kmph. What is the frequency of sound reflected by the submarine? Take the speed of sound in water to be 1450 ms-1.\n",
        "input": "Apparent frequency = [(Speed of sound in air + Speed of enemy submarine)/Speed of sound in air]*Original Frequency",
        "output": "7.18e+04 hertz\nTo calculate the frequency of sound reflected by the submarine in the SONAR system, we need to consider the Doppler effect due to the relative motion between the submarines. The Doppler effect accounts for the change in frequency observed when the source of sound and the observer are in relative motion.The formula to calculate the frequency observed by the submarine is: f' = f * (v_sound / (v_sound - v_sub)), where f' is the observed frequency, f is the emitted frequency, v_sound is the speed of sound in water, and v_sub is the velocity of the submarine."
    },
    {
        "instruction": "A convex lens produces a virtual image of height 922 cm of a real object of height 838 cm placed in front of it. What is the magnification of the lens?",
        "input": "Formula: m = hi / ho",
        "output": "To calculate the magnification of the lens, we use the formula m = hi / ho, where m is the magnification, hi is the height of the image, and ho is the height of the object. By substituting the given values into the formula, we can solve for m. In this case, the magnification of the lens is 1.1., this is the final The magnification of the lens is 1.1."
    },
    {
        "instruction": "How much time will a car travelling with a constant velocity of 551 m/s take to travel a distance of 8949 m?",
        "input": "s = 8949 m, v = 551 m/s",
        "output": "The car will take 16.2 s to travel the distance."
    },
    {
        "instruction": "An image is formed by a convex lens of focal length 381 cm at a distance of 984 cm behind it. Find at what distance object is placed in front of lens.",
        "input": "Formula: 1/f = 1/v - 1/u for convex lens.",
        "output": "To find the distance of the object from the lens, we use the formula for convex lenses: 1/f = 1/v - 1/u, where f is the focal length ofthe lens, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 621.7 cm from the lens., this is the final The object is placed at 621.7 cm in front of the lens."
    },
    {
        "instruction": "What is the gravitational potential at the center of the uniform solid sphere of radius 547 m and mass 201 kg?",
        "input": "Gravitational Potential (V) = cal3(201, 547) joule/kg",
        "output": "The gravitational potential at the center of the uniform solid sphere of radius 547 m and mass 201 kg is given by the formula V = (-3 * G * m) / (2 * r), where G is the gravitational constant, m is the mass, and r is the distance. Plugging in the values, we get V = -3.68e-11 joule/kg."
    },
    {
        "instruction": "A satellite of mass 449 kg orbits around a planet at a height of 3000 m from the surface of the planet. What is the gravitational potential energy on the satellite due to the planet's magnetic field? Mass of the planet = 740000000000 kg and radius of the planet = 5000000 m.",
        "input": "Gravitational -M / (h + R)",
        "output": "The gravitational potential energy on the satellite due to the planet's magnetic field is approximately -1.48e+05 joules."
    },
    {
        "instruction": "About 86 percent of the power of a 261 W light bulb is converted to visible radiation. What is the average intensity of the visible radiation at a distance of 144 m from the bulb?\n",
        "input": "Average Intensity = (Percentage Power / Total Power) / (4 * pi * distance^2)",
        "output": "1.26e-04 watt/m2\n\n\nThe average intensity of the visible radiation at a distance 'd' from the bulb can be calculated using the formula Average Intensity = (Percentage Power / Total Power) / (4 * pi * distance^2), where Percentage Power is the percentage of power converted to visible radiation, Total Power is the total power of the light bulb, and 'd' is the distance from the bulb."
    },
    {
        "instruction": "A regular 4-gon with a distance between each vertex and the center as 170 cm has a charge of 386 micro-Coulombs at each of its vertices. Calculate the potential at the center of the 4-gon?",
        "input": "Formula: 9 * 10^9 * n * (q1 * 10^(-6)) * (1 / (d * 0.01))\nValues: n = 4, q1 = 386 micro-C, d = 170 cm",
        "output": "Answer: 8.17e+06 volt\n\nExplanation:\nThe potential at the center of the 4-gon can be calculated using the formula:\n\nV = k * n * q1 / d\n\nwhere k is the electrostatic constant (9 * 10^9 Nm^2/C^2), n is the number of vertices, q1 is the charge at each vertex, and d is the distance between each vertex and the center.\n\nSubstituting the given values, we have:\n\nV = 9 * 10^9 * 4 * (386 * 10^(-6)) / (170 * 0.01) = 8.17e+06 volt"
    },
    {
        "instruction": "Assuming the Earth to be a sphere of uniform mass density, how much would a body weigh 75/110 down to the center of the Earth if it weighed 282 N on the surface?",
        "input": "Weight on the Surface (W) = 282 N, Height Ratio (n/d) = 75/110",
        "output": "The weight of the body 75/110 down to the center of the Earth, assuming a uniform mass density, would be 89.7 newtons."
    },
    {
        "instruction": "A sound produces 927 crests and 927 troughs in 63 seconds. When the first trough is produced, the first crest is 1870 m away from the source, then calculate the wave speed ?\n",
        "input": "Wavelength = Speed*Time Period, ",
        "output": "59.4 m/s\nTo calculate the speed of sound, we need to determine the distance traveled by a crest or trough in the given time interval. In 63 seconds, 927 crests and 927 troughs are produced. This means that one complete cycle of the wave (a crest and a trough) occurs 927 times in 63 seconds. Therefore, the time taken for one complete cycle (T) can be calculated as: T = 63 s / 927 cycles. The distance traveled by one complete cycle (wavelength, \u03bb) is given by the formula: \u03bb = speed * T, where speed is the speed of sound. Since the first crest is 1870 m away from the source, the distance traveled by a complete cycle (\u03bb) can be expressed as: \u03bb = 1870 m + 1870 m = 2 * 1870 m. Substituting the value of \u03bb and T into the equation, we can calculate the speed of sound: speed = \u03bb / T = (2 * 1870 m) / (63 s / 927 cycles). Calculating this expression will give us the speed of sound."
    },
    {
        "instruction": "A 53 cm long metallic rod is rotated with an angular frequency of 137 rad s-1 about an axis normal to the rod passing through one of its ends. The other end of the rod is in contact with a circular metallic ring. A uniform magnetic field of 30 T parallel to the axis exists everywhere. Find the EMF developed between the center and the ring.\n",
        "input": "EMF = (B * l * w^2) / 2",
        "output": "1.49e+07 volt\n\n\nThe electromotive force (EMF) can be calculated using the formula EMF = (B * l * w^2) / 2, where B is the magnetic field magnitude, l is the length of the metallic rod, and w is the angular frequency of rotation in radians per second."
    },
    {
        "instruction": "A concave lens produces 19 times diminished real image of an object of height 989 cm placed in front of it. What is the height of the image formed by it?",
        "input": "Formula: hi = ho / n",
        "output": "To find the height of the image formed by the concave lens, we use the formula hi = ho / n, where hi is the height of the image, ho is the height of the object, and n is the magnification factor. By substituting the given values into the formula, we can solve for hi. In this case, the height of the image formed by it is 52.1 cm., this is the final The height of the image formed by it is 52.1 cm."
    },
    {
        "instruction": "A hospital uses an ultrasonic scanner to locate tumours in a tissue. What is the wavelength of sound in a tissue in which the speed of sound is 2736 kms-1? The operating frequency of the scanner is 2750 kHz.?\n",
        "input": "Wavelength of tissue = speed of sound in wave/operating frequency of scanner",
        "output": "9.95e-04 m\nTo calculate the wavelength of sound in a tissue, we can use the formula: \u03bb = v / f, where \u03bb is the wavelength, v is the speed of sound, and f is the frequency."
    },
    {
        "instruction": "An object moving with a speed of 372 kmph covers x m in 543 s, then find the value of x?\n",
        "input": "Distance = Speed*Time",
        "output": "56110.0\nDistance = Speed*Time"
    },
    {
        "instruction": "The coefficient of linear expansion of brass is 6.000000000000001e-05 K^-1. What is the change in its volume 15 m^3 for a rise in temperature from 57 degree C to 260 degree C?",
        "input": "Change in volume = d1 * a * (t2 - t1)",
        "output": "To find the change in volume, we use the following formula:\n\nChange in volume = d1 * a * (t2 - t1)\n\nSubstituting the given values into the formula, we find that the change in volume is approximately 0.18 m^3."
    },
    {
        "instruction": "If a car attains a velocity of 796 m/s by applying a constant acceleration of 33 m/s\u00b2 for 1 s, then what is the initial velocity of the car?",
        "input": "initial_velocity = final_velocity - (acceleration * time)",
        "output": "The initial velocity of the car is 763 m/s."
    },
    {
        "instruction": "Two objects of masses 3 g and 5 g are moving along the same line and direction with velocities of 27 m/s and 9 m/s respectively. They collide and after the collision, the first object moves at a velocity of 3 m/s. Determine the initial velocity of the first object.",
        "input": "u1 = ((m1 * v1) + (m2 * v2) - (m2 * u2)) / m1",
        "output": "To find the initial velocity of the first object (u1), we use the formula:\n\nu1 = ((m1 * v1) + (m2 * v2) - (m2 * u2)) / m1\n\nSubstituting the given values, we have:\n\nu1 = ((3 * 3) + (5 * 18) - (5 * 9)) / 3\n\nSimplifying the expression gives us u1 = -12.0 m/s."
    },
    {
        "instruction": "Two absolute scales A and B have triple points of water defined to be 707 A and -132 B. What is the relation between TA and TB?",
        "input": "Relation between TA and TB = TA / TB",
        "output": "To find the relation between TA and TB, we divide the temperature on scale A (TA) by the temperature on scale B (TB). Therefore, the relation is given by:\n\nRelation between TA and TB = TA / TB\n\nSubstituting the given values, we find that the relation is approximately -5.36."
    },
    {
        "instruction": "A toroid has a core of inner radius 141 cm and outer radius 178 cm, around which 291 turns of a wire are wound. If the current in the wire is 2 A, what is the magnetic field inside the core of the solenoid.",
        "input": "Magnetic field = (mu * n * i) / l",
        "output": "To calculate the magnetic field inside the toroid, we use the following formula:\n\nMagnetic field = (mu * n * i) / l\n\nWhere,\n- n = Number of turns of the wire\n- i = Current in the wire\n- l = Length of the wire\n\nWe calculate the length of the wire using the formula:\n- Length of the wire = (r1 + r2) * pi\n\nSubstituting the given values and evaluating the formula, we find that the magnetic field inside the core of the toroid is approximately 7.30e-05 tesla."
    },
    {
        "instruction": "What is the electric field at the centre of the uniform solid sphere of radius 160 m and having 1.18e-06 C charge distributed uniformly.",
        "input": "Electric Field (E) = 0 N/C",
        "output": "0 newton/coulomb\nFor a uniformly charged solid sphere, the electric field at the center is zero."
    },
    {
        "instruction": "A short bar magnet of magnetic moment 9.04 J/T is placed in a uniform magnetic field of 16.54 T. If the magnet is free to rotate in the plane of the field, what is the potential energy of the magnet at a position making an angle of 22 degrees with the magnetic field?",
        "input": "-m * b * 0.93",
        "output": "The potential energy of the magnet at a position making an angle of 0.9271838545667874 degrees with the magnetic field can be calculated using the formula -m * b * cos(d), where 'm' is the magnetic moment of the bar magnet, 'b' is the magnetic field strength, and 'd' is the angle. Substituting the given values, we have -(9.04) * 16.54 * 0.93 = -1.39e+02 joule."
    },
    {
        "instruction": "If a diatomic gas of 5 moles at 28 atm and volume 122 lit is adiabatically changed to pressure 13 atm, then what will be its volume.\n",
        "input": "P1*(V1^1.4)=P2*(V2^1.4)",
        "output": "211.0lit\nTo calculate the final pressure of the diatomic gas after an adiabatic expansion, we can use the adiabatic equation: P1 * V1^\u03b3 = P2 * V2^\u03b3, where P1 and V1 are the initial pressure and volume, P2 and V2 are the final pressure and volume, and \u03b3 is the heat capacity ratio. The heat capacity ratio (\u03b3) for a diatomic gas is typically 7/5."
    },
    {
        "instruction": "A pump on the ground floor of a building can pump up water to fill a tank of volume 76 m3 in 23 min. If the tank is 18 m above the ground, and the efficiency of the pump is 5%, how much electric power is consumed by the pump?\n",
        "input": "(100000*v*h*9.8)/(t*e)",
        "output": "To find the electricity in the pump: (100000*v*h*9.8)/(t*e), this is the final answer 194295.65watts\n"
    },
    {
        "instruction": "Two gold pieces of masses are 377.35 g and 3730.03 g respectively. What is the difference of the masses of the pieces to correct significant figures?\n",
        "input": "",
        "output": "3.3526e+03\n"
    },
    {
        "instruction": "A circular coil of radius 9 cm consists of 26 turns and carries a current of 8 A. The coil is suspended vertically, and the normal to the plane of the coil makes an angle of 24 degrees with the direction of a uniform horizontal magnetic field of magnitude 9 tesla. What is the magnitude of the torque experienced by the coil.",
        "input": "Torque = n * b * i * A * sin(d)",
        "output": "To calculate the magnitude of the torque experienced by the coil, we use the following formula:\n\nTorque = n * b * i * A * sin(d)\n\nWhere,\n- n = Number of turns in the coil\n- b = Magnetic field\n- i = Current in the coil\n- A = Area of the coil\n- d = Angle between the normal to the coil and the magnetic field\n\nFor a square coil, the area (A) is equal to the square of the side length (l) of the coil. For a circular coil, the area (A) is equal to pi times the square of the radius (l) of the coil.\n\nSubstituting the given values into the formula and evaluating it, we find that the magnitude of the torque experienced by the coil is approximately 19.4 newton-m."
    },
    {
        "instruction": "A bullet of mass 75 kg and horizontal speed 32 m/s strikes a block of wood of mass 59 kg and instantly comes to rest with respect to the block. Estimate the amount of heat produced in the block.",
        "input": "Heat = K1 - K2",
        "output": "To calculate the amount of heat produced, we use the formula Heat = K1 - K2, where K1 is the initial kinetic energy of the bullet and K2 is the final kinetic energy of the system after the collision., this is the final answer -671299.4"
    },
    {
        "instruction": "A 130 pF capacitor is charged by a 127 V supply. It is then disconnected from the supply and is connected to another uncharged 160 pF capacitor. How much electrostatic energy is lost in this process?",
        "input": "Formula: (1048385.0 - 578419.3103448276) * 10^(-12)\nValues: c1 = 130 pF, c2 = 160 pF, v = 127 V",
        "output": "Answer:4.70e-07 joule\n\nExplanation: The electrostatic energy lost in the process can be calculated by subtracting the final energy from the initial energy:\n\nE_loss = E_initial - E_final\n\nThe initial energy E_initial can be calculated as 0.5 * C1 * V^2, where C1 is the capacitance of the first capacitor and V is the voltage. The final energy E_final can be calculated as 0.5 * C3 * V^2, where C3 is the equivalent capacitance when the two capacitors are combined.\n\nSubstituting the given values, we have:\n\nE_loss = 1048385.0 joule - 578419.3103448276 joule = E_loss = 4.70e-07 joule joule."
    },
    {
        "instruction": "A photon of energy 1539 eV strikes on metal surface ; the work function of the metal being 695 eV. Calculate the kinetic energy of the emission and the velocity of the photoelectron. (Given 1 eV = 1.6020 \u00d7 10-19 J).\n",
        "input": "Kinetic Energy = Energy of Photon - Work Function of Metal",
        "output": "kinetic energy of ejected photoelectron = energy of photon - workfunction = 1539 - 695 = 844 joules and if m is mass of ejected electron then velocity of ejected photo electron = sq.root((ke x 2)/m) = sq.root((844 x 2)/9.1e-31) = 1.72e+07 m/s\nTo calculate the kinetic energy of the emitted photoelectron and its velocity, we need to apply the principle of conservation of energy. The energy of the incident photon is used to overcome the work function of the metal and provide kinetic energy to the emitted electron.v = sqrt((2 * Kinetic energy) / m), Substituting the calculated kinetic energy and the electron mass into the equation will give us the velocity of the photoelectron."
    },
    {
        "instruction": "An aircraft of mass 52 kg executes a horizontal loop at a speed of 221 m/s with its wings banked at 15 degrees. What is the radius of the loop?",
        "input": "(v^2) / (g * tan((param * pi) / 180))",
        "output": "18228\nTo calculate the radius, we use the formula (v^2) / (g * tan((param * pi) / 180)), where v is the speed (221 m/s), g is the acceleration due to gravity (10 m/s^2), and param is the angle of banking (15 degrees)."
    },
    {
        "instruction": "An electric appliance of 1569 W power is operated in a domestic circuit of 227 V. What is the minimum current rating it should have to avoid overloading?",
        "input": "P/V",
        "output": "The minimum current rating required = P/V = 1569/227 = 6.9 ampere."
    },
    {
        "instruction": "In a process, 5594 J of heat is released by a system and 7886 J of work is done by the system. What is the change in internal energy for the process ?\n",
        "input": "\u0394U = Q+W",
        "output": "from first law of thermodynamics, du = q + w => du = (-5594) + (-7886) => du = -13480joule\nQ is negative and W is negative as heat is released by a system and work is done by system."
    },
    {
        "instruction": "What is the gravitational field at a point P at a distance of 441 m from the center of the uniform solid sphere of radius 493 m and mass 85 kg?",
        "input": "Gravitational Field (g) = cal2(85, 441, 493) N/kg",
        "output": "The gravitational field at a point P at a distance of 441 m from the center of the uniform solid sphere of radius 493 m and mass 85 kg is given by the formula g = (-G * m) / (r^2), where G is the gravitational constant, m is the mass, and r is the distance. Plugging in the values, we get g = -2.92e-14 N/kg."
    },
    {
        "instruction": "On a long horizontally moving belt, a child runs to and fro with a speed of 48 ms-1 (with respect to the belt) between his parents located 197 m apart on the moving belt. The belt moves with a speed of 31 ms-1. For an observer on a stationary platform outside, what is the speed of the child running opposite to the direction of motion of the belt?",
        "input": "speed_child = speed_relative - speed_belt",
        "output": "The speed of the child running opposite to the direction of motion of the belt is 17 ms-1."
    },
    {
        "instruction": "At t = 0, a wheel is rotating with an angular velocity of 33 rad/s at a constant angular acceleration of 8 rad/s\u00b2. It attains an angular velocity of 69 rad/s. What is the value of t in seconds?",
        "input": "time = (final_angular_velocity - initial_angular_velocity) / angular_acceleration",
        "output": "To calculate the time, we use the following formula:\n\ntime = (final_angular_velocity - initial_angular_velocity) / angular_acceleration\n\nSubstituting the given values into the formula, we find that the time is approximately 4.5 seconds."
    },
    {
        "instruction": "A body is dropped from the top of a building with an initial velocity of 3160 m/s under gravity, and it reaches the ground after 160 s. What is the height of the building?",
        "input": "initial velocity (u) = 3160 m/s, time (t) = 160 s",
        "output": "height (s) = initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)\u00b2\ns = 3160 * 160 + 0.5 * 9.8 * 160\u00b2\ns = 505600 + 125440.00000000001\ns = 631040.0"
    },
    {
        "instruction": "Calculate the energy of each of the photons which correspond to light of frequency 656172 Hz.\n",
        "input": "Energy = h*frequency",
        "output": "4.33e-28joules\nTo calculate the energy of a photon, you can use the formula: E = h * f, where E is the energy of the photon, h is the Planck constant (approximately 6.626 x 10^-34 J\u00b7s), and f is the frequency of the light."
    },
    {
        "instruction": "A truck starts from rest and accelerates uniformly at 20 ms-2. At t = 104 s, a stone is dropped by a person standing on the top of the truck (14 m high from the ground). What are the (a) velocity, and (b) acceleration of the stone at t = 131 s? (Neglect air resistance.)",
        "input": "A truck starts from rest and accelerates uniformly at 20 ms-2. At t = 104 s, a stone is dropped by a person standing on the top of the truck (14 m high from the ground). What are the (a) velocity, and (b) acceleration of the stone at t = 131 s? (Neglect air resistance.)",
        "output": "Velocity is 2097.5 ms-1, at an angle of 7 degrees with horizontal. Acceleration is g (10 ms-2) downwards."
    },
    {
        "instruction": "A steel cable with a radius of 126 mm supports a chairlift at a ski area. If the maximum stress is not to exceed 8547 x 10^(6) Nm-2, what is the maximum load the cable can support?",
        "input": "",
        "output": "The maximum load the cable can support is 4.3e+02 newton."
    },
    {
        "instruction": "The escape speed of a projectile on the Earth's surface is 11.2 km/s. A body is projected out with the speed of 204.938 km/s. What is the speed of the body far away from the Earth?",
        "input": "Projectile Speed : 204.6 km/s km/s",
        "output": "204.6 km/s\n\nExplanation: The speed of the body far away from the Earth, when projected with a speed of 204.6 km/s km/s, can be calculated using the escape speed formula. By substituting the given values, the speed is found to be 204.6 km/s."
    },
    {
        "instruction": "A steam engine delivers 864 J of work per minute and services 1573 J of heat per minute from its boiler. How much heat is wasted per minute?\n",
        "input": "Efficiency = Work per minute/Heat per minute from its boiler, Heat Wasted = Heat per minute - (Efficiency/100)*Heat per minute",
        "output": "709 joules\nThe efficiency of an engine can be calculated using the formula: Efficiency = (Work output / Heat input) * 100"
    },
    {
        "instruction": "An Electric Iron of resistance 98 ohm takes a current of 9 A, if the heat developed is 1910 J, then what is the time taken?",
        "input": "t = energy / (I^2 * R)",
        "output": "To calculate the time taken, we rearrange the formula t = energy / (I^2 * R) to solve for t. Substituting the values, where energy is 1910 J, I is 9 A, and R is 98 ohm, we can calculate the time., this is the final answer 0.2"
    },
    {
        "instruction": "A convex lens produces a virtual image at a distance of 851 cm from it of a real object placed 423 cm in front of it. What is the magnification of the lens?",
        "input": "Formula: m = v / u",
        "output": "To calculate the magnification of the lens, we use the formula m = v / u, where m is the magnification, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for m. In this case, the magnification of the lens is 2.0., this is the final The magnification of the lens is 2.0."
    },
    {
        "instruction": "Suppose that the electric field amplitude of an electromagnetic wave is E0 = 64 N/C and that its frequency is v = 1022 MHz. Determine wavelength?",
        "input": "v = 1022 MHz",
        "output": "0.29 m\n\nThe wavelength can be calculated by dividing the speed of light by the frequency."
    },
    {
        "instruction": "The coefficient of volume expansion of copper is 5.1e-05 K^-1. What is the change in its volume 73 m^3 for a rise in temperature from 43 degree C to 222 degree C?",
        "input": "Change in volume = d1 * a * (t2 - t1)",
        "output": "To find the change in volume, we use the following formula:\n\nChange in volume = d1 * a * (t2 - t1)\n\nSubstituting the given values into the formula, we find that the change in volume is approximately 0.67 m^3."
    },
    {
        "instruction": "A body is dropped from the top of a building with an initial velocity of 830 m/s under gravity, and it reaches the ground after 142 s. What is the height of the building?",
        "input": "initial velocity (u) = 830 m/s, time (t) = 142 s",
        "output": "height (s) = initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)\u00b2\ns = 830 * 142 + 0.5 * 9.8 * 142\u00b2\ns = 117860 + 98803.6\ns = 216663.6"
    },
    {
        "instruction": "Find the focal length of a concave mirror whose radius of curvature is 2653.56 cm.",
        "input": "Formula: f = R/2",
        "output": "To find the focal length of a concave mirror, we use the formula f = R/2, where f is the focal length and R is the radius of curvature. By substituting the given value of R into the formula, we can solve for f. In this case, the focal length is 1326.8 cm., this is the final 1326.8"
    },
    {
        "instruction": "A tank is filled with water to a height of 125.6 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 111.8 cm. What is the refractive index of water?",
        "input": "Formula: refractive index = height of tank / apparent depth of needle",
        "output": "To calculate the refractive index, we use the formula: refractive index = height of tank / apparent depth of needle. In this case, the height of the tank is 125.6 cm and the apparent depth of the needle is 111.8 cm., this is the final 1.12"
    },
    {
        "instruction": "A parallel plate capacitor made of circular plates of radius r = 83 cm has a capacitance C = 28 pF. The capacitor is connected to a 230 V ac supply with an angular frequency of 440 rad/s. Determine the amplitude of B at a point 6 cm from the axis between the plates?",
        "input": "d = 6 cm, r = 83 cm, I = 2.83e-06 ampere",
        "output": "6.98e-14 tesla\n\nThe amplitude of the magnetic field at a point between the plates can be calculated using the formula: B = (\u03bc\u2080dI\u2080) / (r\u00b2), where \u03bc\u2080 is the permeability of free space, d is the distance from the axis, I\u2080 is the rms current, and r is the radius of the plates."
    },
    {
        "instruction": "6 capacitors each of capacitance 90pF are connected in parallel. What is the total capacitance of the combination when the system is connected to a 217 V supply?\n",
        "input": "C_total = C1 + C2 + C3 + ... + Cn\n",
        "output": "5.40e+02 pico-farad\n\nExplanation: C_total = 90 + 90 + 90 + ... + 90 = 5.40e+02 pico-farad\n"
    },
    {
        "instruction": "A hole is drilled in a steel sheet. The diameter of the hole is 19 cm at 110 degree C. What is the change in the diameter of the hole when the sheet is heated to 289 degree C? Coefficient of linear expansion of steel = 1.2 x 10-5K-1.",
        "input": "Change in diameter = initial diameter * sqrt(1 + (coefficient of linear expansion * initial diameter * (final temperature - initial temperature))) - initial diameter",
        "output": "To calculate the change in diameter, we use the following formula:\n\nChange in diameter = initial diameter * sqrt(1 + (coefficient of linear expansion * initial diameter * (final temperature - initial temperature))) - initial diameter\n\nSubstituting the given values into the formula, we find that the change in diameter is approximately 0.384 cm."
    },
    {
        "instruction": "A square coil of side 30 cm consists of 28 turns and carries a current of 8 A. The coil is suspended vertically, and the normal to the plane of the coil makes an angle of 64 degrees with the direction of a uniform horizontal magnetic field of magnitude 11 tesla. What is the magnitude of the torque experienced by the coil.",
        "input": "Torque = n * b * i * A * sin(d)",
        "output": "To calculate the magnitude of the torque experienced by the coil, we use the following formula:\n\nTorque = n * b * i * A * sin(d)\n\nWhere,\n- n = Number of turns in the coil\n- b = Magnetic field\n- i = Current in the coil\n- A = Area of the coil\n- d = Angle between the normal to the coil and the magnetic field\n\nFor a square coil, the area (A) is equal to the square of the side length (l) of the coil. For a circular coil, the area (A) is equal to pi times the square of the radius (l) of the coil.\n\nSubstituting the given values into the formula and evaluating it, we find that the magnitude of the torque experienced by the coil is approximately 199.3 newton-m."
    },
    {
        "instruction": "Calculate the energy of each of the photons which correspond to light of frequency 30387 Hz.\n",
        "input": "Energy = h*frequency",
        "output": "2.01e-29joules\nTo calculate the energy of a photon, you can use the formula: E = h * f, where E is the energy of the photon, h is the Planck constant (approximately 6.626 x 10^-34 J\u00b7s), and f is the frequency of the light."
    },
    {
        "instruction": "A concave mirror produces 44 times magnified virtual image of a 5.38 cm object placed in front of it. What is the height of the image formed by the mirror?",
        "input": "Formula: hi = n * ho",
        "output": "To find the height of the image formed by the mirror, we use the formula hi = n * ho, where hi is the height of the image, n is the magnification factor, and ho is the height of the object. By substituting the given values into the formula, we can solve for hi. In this case, the height of the image formed by the mirror is 236.7 cm., this is the final The height of the image formed by the mirror is 236.7 cm."
    },
    {
        "instruction": "A series LCR circuit is connected to a variable frequency 230 V source with L = 106 H, C = 128 muF, R = 68 ohm. Determine the source frequency which drives the circuit in resonance?",
        "input": "Source Frequency = 1 / sqrt(L * C)",
        "output": "8.6 rad/s"
    },
    {
        "instruction": "If a physical quantity P=(a^-2.0)*(b^0.5)*(c^-0.5), the percentage errors of measurement in a,b,c are 5%,5%,1% respectively. If the calculated value of P is 3 then what is maximum error possible.\n",
        "input": "Percentage Error in P = |dP/P| * 100",
        "output": "0.39\nTo find the maximum possible error in the calculated value of P, we can use the concept of percentage error propagation. The formula to calculate the percentage error in a quantity calculated from measured quantities is given by: Percentage Error in P = |dP/P| * 100, where dP is the maximum absolute error in P. Since P = (a^-2.0)*(b^0.5)*(c^-0.5), we can differentiate the expression with respect to each measured quantity (a, b, c) to find the maximum absolute error for each term. Then we can substitute the given percentage errors and calculated value of P to find the maximum error. Let's calculate the maximum error using the given information."
    },
    {
        "instruction": "If a gas molecule has root mean square velocity of 1556 m/s and is at a temperature 1 degree C. What is the molar mass of the gas.",
        "input": "(3 * r * t1 * 1000) / (v * v)",
        "output": "11.06908079513088 m/s\n The formula used is: (3 * r * t1 * 1000) / (v * v)"
    },
    {
        "instruction": "Two bodies A and B of masses 5 kg and 13 kg are in contact with each other rest on a table against a rigid wall (such that B is attached to the wall). The coefficient of friction between the bodies and the table is 0.26. A force of 159 N is applied horizontally to A. Then what is the value of action-reaction forces between A and B.",
        "input": "",
        "output": "159 newton"
    },
    {
        "instruction": "A convex lens produces 54 times magnified virtual image of an object at a distance of 2233 cm from the lens. At what distance is the object placed in front of the lens?",
        "input": "Formula: u = v / n",
        "output": "To find the distance at which the object is placed in front of the lens, we use the formula u = v / n, where u is the distance of the object from the lens, v is the distance of the image from the lens, and n is the magnification factor. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 41.4 cm in front of the lens., this is the final The object is placed at a distance of 41.4 cm in front of the lens."
    },
    {
        "instruction": "For an amplitude modulated wave, the maximum amplitude is found to be 13.06 V while the minimum amplitude is found to be 5.03 V. Determine the modulation index.\n",
        "input": "Modulation index = (a_max - a_min) / (a_max + a_min)",
        "output": "To determine the modulation index of an amplitude modulated wave, we use the formula modulation index = (a_max - a_min) / (a_max + a_min). Given the maximum amplitude (a_max) = 13.06 V and the minimum amplitude (a_min) = 5.03 V, the modulation index is equal to 0.44\n"
    },
    {
        "instruction": "A parallel plate capacitor made of circular plates of radius r = 26 cm has a capacitance C = 118 pF. The capacitor is connected to a 230 V ac supply with an angular frequency of 330 rad/s. Determine the amplitude of B at a point 3 cm from the axis between the plates?",
        "input": "d = 3 cm, r = 26 cm, I = 8.96e-06 ampere",
        "output": "1.12e-12 tesla\n\nThe amplitude of the magnetic field at a point between the plates can be calculated using the formula: B = (\u03bc\u2080dI\u2080) / (r\u00b2), where \u03bc\u2080 is the permeability of free space, d is the distance from the axis, I\u2080 is the rms current, and r is the radius of the plates."
    },
    {
        "instruction": "An Electric Iron of resistance 47 ohm takes a current of 7 A, then what is the heat developed in 781 s?",
        "input": "Heat = I^2 * R * t",
        "output": "To calculate the heat developed in the Electric Iron, we use the formula Heat = I^2 * R * t, where I is the current (7 A), R is the resistance (47 ohm), and t is the time (781 s)., this is the final answer 1798643"
    },
    {
        "instruction": "If a wheel of radius 81 m has an angular acceleration of 209 rad/s\u00b2, what is the acceleration of a point at the circumference of the wheel?",
        "input": "acceleration_at_circumference = angular_acceleration * radius",
        "output": "To calculate the acceleration at the circumference, we use the following formula:\n\nacceleration_at_circumference = angular_acceleration * radius\n\nSubstituting the given values into the formula, we find that the acceleration at the circumference is approximately 16929 m/s\u00b2."
    },
    {
        "instruction": "The volume of 1819 g of a substance is 5 cm\u00b3. If the density of the liquid in which the substance is placed is 6 g/cm\u00b3, will the substance float or sink?",
        "input": "Density of Substance = 363.8 g/cm\u00b3, Density of Liquid = 6 g/cm\u00b3",
        "output": "The substance will sink."
    },
    {
        "instruction": "A 78 kg girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter 13516 micrometer. What is the pressure exerted by the heel on the horizontal floor?",
        "input": "78 * 9.8 / 0.00014347830834770246",
        "output": "The pressure exerted by the heel on the horizontal floor is 5.33e+06 newton. The pressure exerted by the heel on the horizontal floor is calculated using the formula P = (m * 9.8) / A, where m is the mass of the girl (78 kg) and A is the area of the heel (0.00014347830834770246 m^2)."
    },
    {
        "instruction": "A convex mirror produces 19 times diminished real image of an object at a distance of 64 cm from the mirror. At what distance is the object placed in front of the mirror?",
        "input": "Formula: u = v * n",
        "output": "To find the distance at which the object is placed in front of the mirror, we use the formula u = v * n, where u is the distance of the object from the mirror, v is the distance of the image from the mirror, and n is the magnification factor. By substituting the given values into the formula, we can calculate u. In this case, the object is placed at a distance of 1216 cm in front of the mirror., this is the final The object is placed at a distance of 1216 cm in front of the mirror."
    },
    {
        "instruction": "14 capacitors each of capacitance 77pF are connected in series. What is the total capacitance of the combination when the system is connected to a 165 V supply?\n",
        "input": "1 / C_total = 1 / C1 + 1 / C2 + 1 / C3 + ... + 1 / Cn\n",
        "output": "5.50e+00 pico-farad\n\nExplanation: 1 / C_total = 1 / 77 + 1 / 77 + 1 / 77 + ... + 1 / 77\n"
    },
    {
        "instruction": "Monochromatic light of wavelength of 4305 nm is incident on aa surface of refractive index 430.5. What is the wavelength, speed and frequenct of reflected light.\n",
        "input": "frequency = c/wavelength",
        "output": "4305.0 nm , 3.00e+08 m/s and 6.97e+13 hz \nThe ray will reflect back in the same medium as that of incident ray. Hence, the wavelength, speed, and frequency of the reflected ray will be the same as that of the incident ray."
    },
    {
        "instruction": "A wire of material-1 of cross-sectional area 13 x 10^(-6) m^2 stretches by the same amount as a wire of material-2 of cross-sectional area 17 x 10^(-6) m^2 under a given load. What is the ratio of the Young\u2019s modulus of material-1 to that of material-2, assuming the ratio of their lengths is 168/33?",
        "input": "ratio = (l1 * A2) / (l2 * A1)",
        "output": "The ratio of the Young's modulus of material-1 to that of material-2 is approximately 6.66. To calculate the ratio, we use the formula:\n\nratio = (l1 * A2) / (l2 * A1)"
    },
    {
        "instruction": "A stone of mass 682 g dropped from the top of a tower of height 354 m high splashes into the water of a pond near the base of the tower. When is the splash heard at the top given.\n",
        "input": "Height = Initial Speed + 1/2*g*time^2, Total time = t1+t2",
        "output": "9.54 s\nUse the equation of motion: Height = Initial Speed + 1/2*g*time^2, to calculate the time of splash heard."
    },
    {
        "instruction": "If a particle of mass 510 g is in linear SHM with w = 179, amplitude 136 cm then find average kinetic energy over a period.\n",
        "input": "0.25*m*0.001*w*w*amp*amp*0.0001",
        "output": "use the formula (0.25*m*0.001*w*w*amp*amp*0.0001), this is the final answer: 7.56e+03 joule\n"
    },
    {
        "instruction": "At t = 0, a wheel is rotating with an angular velocity of 329 rad/s at a constant angular acceleration. It attains an angular velocity of 439 rad/s in t = 12 sec. What is the value of the angular acceleration?",
        "input": "angular_acceleration = (final_angular_velocity - initial_angular_velocity) / time",
        "output": "To calculate the angular acceleration, we use the following formula:\n\nangular_acceleration = (final_angular_velocity - initial_angular_velocity) / time\n\nSubstituting the given values into the formula, we find that the angular acceleration is approximately 9.2 rad/s\u00b2."
    },
    {
        "instruction": "A radio can tune over the frequency range of a portion of MW broadcast band: (403 kHz to 613 kHz). If its LC circuit has an effective inductance of 133 muH, what must be the range of its variable capacitor?",
        "input": "w1 = 2 * pi * f1\nC1 = 1 / ((w1 ** 2) * L)\nw2 = 2 * pi * (f1 + f2)\nC2 = 1 / ((w2 ** 2) * L)",
        "output": "5.07e-10 farad to 1.17e-09 farad"
    },
    {
        "instruction": "Suppose that the electric field part of an electromagnetic wave in vacuum is E = 916cos[1694y + 177096t]. Write an expression for the magnetic field part of the wave?",
        "input": "B0 = 3.05e-06 tesla, k = 1694, w = 177096",
        "output": "3.05e-06cos[1694y + 177096t]\n\nThe expression for the magnetic field part of the wave can be written as B = B0cos[ky + wt]."
    },
    {
        "instruction": "Calculate the enthalpy change on freezing of 10 mol of water at 79.1 celcius to ice at -82.3 celcius.\n",
        "input": "(\u0394H)=(\u0394H1)+(\u0394H2)",
        "output": "89576.0\nTotal enthalpy change involved in the transformation is the sum of the following changes and can be represented using the Hess Law."
    },
    {
        "instruction": "What is the gravitational field at a point P on the surface of the uniform solid sphere of radius 325 m and mass 107 kg?",
        "input": "Gravitational Field (g) = cal3(107, 325) N/kg",
        "output": "The gravitational field at a point P on the surface of the uniform solid sphere of radius 325 m and mass 107 kg is given by the formula g = (-G * m) / (r^2), where G is the gravitational constant, m is the mass, and r is the distance. Plugging in the values, we get g = -6.76e-14 N/kg."
    },
    {
        "instruction": "Two point charges q1 = 113 x 10^(-6)C and q2 = - 113 x 10^(-6)C are located at the points A:(0, 0, - 13 cm) and B:(0, 0, -170 cm), respectively. What are the total charge and electric dipole moment of the system?\n",
        "input": "Total charge = 0\nElectric dipole moment = q1 * d",
        "output": "The total charge of the system is 0 coulomb and the electric dipole moment is 2.07e-04 coulomb-m\n"
    },
    {
        "instruction": "A batsman deflects a ball by an angle of 49 degrees without changing its initial speed, which is equal to 199 m/s. What is the impulse imparted to the ball? (The mass of the ball is 171 g)",
        "input": "Impulse calculation",
        "output": "44.7\nThe impulse imparted to the ball can be calculated using the formula (2 * mass * velocity * cos(angle)) / 1000, where the mass is 171 g, the velocity is 199 m/s, and the angle is 49 degrees. The result is 44.7 kg\u00b7m/s, perpendicular to the point of impact on the bat."
    },
    {
        "instruction": "A convex lens produces 82 times diminished real image of an object at a distance of 24.96 cm from the lens. At what distance is the object placed in front of the lens?",
        "input": "Formula: u = v * n",
        "output": "To find the distance at which the object is placed in front of the lens, we use the formula u = v * n, where u is the distance of the object from the lens, v is the distance of the image from the lens, and n is the magnification factor. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 2046.7 cm in front of the lens., this is the final The object is placed at a distance of 2046.7 cm in front of the lens."
    },
    {
        "instruction": "What is the focal length of a concave lens of focal length 431 cm in contact with a convex lens of focal length 430 cm? Is the system a converging or a diverging lens? Ignore thickness of the lenses.",
        "input": "Formula: For two lenses in contact, the combined focal length (P) is given by P = (f1 * f2) / (f1 + f2), where f1 and f2 are the focal lengths of the lenses.",
        "output": "This is the answer {answer}, formula used is : {formula}"
    },
    {
        "instruction": "A force applied on a subject causes 602 m displacement in the direction of the force. If work done is equal to 9366 J, then what is the value of force?",
        "input": "F = W / s",
        "output": "Using the formula: F = W / s, the final answer is: {'answer': '15.6 N', 'explanation': 'To calculate the force, we use the formula F = W / s, where F is the force, W is the work done (9366 J), and s is the displacement (602 m).'}"
    },
    {
        "instruction": "A convex mirror produces 63 times diminished real image of height 0.21 cm of an object placed in front of it. What is the height of the object taken?",
        "input": "Formula: ho = hi * n",
        "output": "To find the height of the object taken in front of the convex mirror, we use the formula ho = hi * n, where ho is the height of the object, hi is the height of the image, and n is the magnification factor. By substituting the given values into the formula, we can calculate ho. In this case, the height of the object taken in front of the convex mirror is 13.2 cm., this is the final The height of the object taken in front of the convex mirror is 13.2 cm."
    },
    {
        "instruction": "A photon of energy 804 eV strikes on metal surface ; the work function of the metal being 714 eV. Calculate the kinetic energy of the emission and the velocity of the photoelectron. (Given 1 eV = 1.6020 \u00d7 10-19 J).\n",
        "input": "Kinetic Energy = Energy of Photon - Work Function of Metal",
        "output": "kinetic energy of ejected photoelectron = energy of photon - workfunction = 804 - 714 = 90 joules and if m is mass of ejected electron then velocity of ejected photo electron = sq.root((ke x 2)/m) = sq.root((90 x 2)/9.1e-31) = 5.63e+06 m/s\nTo calculate the kinetic energy of the emitted photoelectron and its velocity, we need to apply the principle of conservation of energy. The energy of the incident photon is used to overcome the work function of the metal and provide kinetic energy to the emitted electron.v = sqrt((2 * Kinetic energy) / m), Substituting the calculated kinetic energy and the electron mass into the equation will give us the velocity of the photoelectron."
    },
    {
        "instruction": "A charge of 9 mC is located at the origin. Calculate the work done in taking a charge 8 nC from a point P(0, 12 cm, 0) to a point Q(14 cm, 0, 0), via a point R(1 cm, 0, 8 cm).",
        "input": "Charge at Origin (q1) = 9 mC + Charge at P (q2) 8 nC + Coordinates of P: (0, 12 cm, 0) + Coordinates of Q : (14 cm, 0, 0) + Coordinates of R : (1 cm, 0, 8 cm)",
        "output": "7.71e-03 joule\nExplanation: The work done in moving a charge between two points is given by the formula W = q1 * q2 * (Vp - Vq), where q1 and q2 are the charges, and Vp and Vq are the potentials at the respective points. The potential difference (Vp - Vq) is calculated as 0.009 * (1 / p - 1 / q). Plugging in the values, we get W = 7.71e-03 joule."
    },
    {
        "instruction": "In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are 74 ms-1 and 36 ms-1. What is the lift on the wing if its area is 1400 cm2? (Take the density of air to be 1.3 kgm-3)",
        "input": "0.5 * 1.3 * (74**2 - 36**2) * (1400 / 10000)",
        "output": "The lift on the wing is 380.38000000000005 newton."
    },
    {
        "instruction": "What is the lowest total resistance that can be secured by combinations of three coils of resistance 54, 87, 72?",
        "input": "R_total = (R1 * R2 * R3) / (R1 * R2 + R2 * R3 + R3 * R1)",
        "output": "The lowest combination of resistances can be obtained by connecting them in parallel. The total resistance is calculated as (54 * 87 * 72) / (54 * 87 + 87 * 72 + 72 * 54) = 22.8 ohm.\n\nTo calculate the lowest combination of resistances, we connect them in parallel. The total resistance (R_total) is given by the formula (R1 * R2 * R3) / (R1 * R2 + R2 * R3 + R3 * R1), where R1, R2, and R3 are the individual resistances."
    },
    {
        "instruction": "An aircraft of mass 167 kg executes a horizontal loop at a speed of 179 m/s with its wings banked at 20 degrees. What is the radius of the loop?",
        "input": "(v^2) / (g * tan((param * pi) / 180))",
        "output": "8803\nTo calculate the radius, we use the formula (v^2) / (g * tan((param * pi) / 180)), where v is the speed (179 m/s), g is the acceleration due to gravity (10 m/s^2), and param is the angle of banking (20 degrees)."
    },
    {
        "instruction": "What is the gravitational potential at a point P on the surface of the uniform solid sphere of radius 36 m and mass 150 kg?",
        "input": "Gravitational Potential (V) = cal3(150, 36) joule/kg",
        "output": "The gravitational potential at a point P on the surface of the uniform solid sphere of radius 36 m and mass 150 kg is given by the formula V = (-G * m) / r, where G is the gravitational constant, m is the mass, and r is the distance. Plugging in the values, we get V = -2.78e-10 joule/kg."
    },
    {
        "instruction": "A uniformly charged conducting sphere of 1072 cm diameter has a surface charge density of 288 micro-C/m\u00b2, then find the charge on the sphere?\n",
        "input": "Charge = Surface charge density * Surface area",
        "output": "To determine the charge on the sphere, we use the formula:\nCharge = Surface charge density * Surface area\nGiven surface charge density = 288 micro-C/m\u00b2, diameter = 1072 cm,\nCharge = 1.04e-01 C\n"
    },
    {
        "instruction": "Find the radius of curvature of a convex mirror whose focal length is 2250.33 cm.",
        "input": "Formula: R = 2 * f",
        "output": "To find the radius of curvature of a convex mirror, we use the formula R = 2 * f, where R is the radius of curvature and f is the focal length. By substituting the given value of f into the formula, we can solve for R. In this case, the radius of curvature is 4500.7 cm., this is the final 4500.7"
    },
    {
        "instruction": "A radio can tune over the frequency range of a portion of MW broadcast band: (1361 kHz to 1690 kHz). If its LC circuit has an effective inductance of 184 muH, what must be the range of its variable capacitor?",
        "input": "w1 = 2 * pi * f1\nC1 = 1 / ((w1 ** 2) * L)\nw2 = 2 * pi * (f1 + f2)\nC2 = 1 / ((w2 ** 2) * L)",
        "output": "4.82e-11 farad to 7.43e-11 farad"
    },
    {
        "instruction": "A meter stick is balanced on a knife edge at its center. When a coin of mass 94 g is put at the 4 mark, the stick is found to be balanced at 85 cm. What is the mass of the meter stick?",
        "input": "Mass = (Left Side) / Distance",
        "output": "The mass of the meter stick is approximately -165.5 g.\nLeft Side = m1 * (t1 - t2) = 94 * (4 - 85)"
    },
    {
        "instruction": "A convex mirror produces a real image of height 93 cm of a real object having a height of 192 cm and placed 32 cm in front of it. At what distance is the image formed from the mirror?",
        "input": "Formula: m = v / u = hi / ho",
        "output": "To find the distance of the image from the mirror, we use the formula m = v / u = hi / ho, where m is the magnification, v is the distance of the image from the mirror, u is the distance of the object from the mirror, hi is the height of the image, and ho is the height of the object. By rearranging the formula, we can calculate v as v = (u * hi) / ho. By substituting the given values into the formula, we find that the image is formed at a distance of 15.5 cm from the mirror., this is the final The image is formed at a distance of 15.5 cm from the mirror."
    },
    {
        "instruction": "At t = 0, a wheel is rotating with an angular velocity of 212 rad/s at a constant angular acceleration of 12 rad/s\u00b2. It attains an angular velocity of 247 rad/s. What is the value of t in seconds?",
        "input": "time = (final_angular_velocity - initial_angular_velocity) / angular_acceleration",
        "output": "To calculate the time, we use the following formula:\n\ntime = (final_angular_velocity - initial_angular_velocity) / angular_acceleration\n\nSubstituting the given values into the formula, we find that the time is approximately 2.9 seconds."
    },
    {
        "instruction": "In a process, change in internal energy of the system is -5693 J. If 6804 J of work is done by the system, what is the amount of heat absorbed by the process ?\n",
        "input": "\u0394U = Q+W",
        "output": "from first law of thermodynamics, du = q + w => q = du - w => q = (-5693) - (-6804) => q = 1111joule\n"
    },
    {
        "instruction": "A charge of 19 mC is located at the origin. Calculate the work done in taking a charge 4 nC from a point P(0, 10 cm, 0) to a point Q(0, 10 cm, 0), via a point R(0, 3 cm, 7 cm).",
        "input": "Charge at Origin (q1) = 19 mC + Charge at P (q2) 4 nC + Coordinates of P: (0, 10 cm, 0) + Coordinates of Q : (0, 10 cm, 0) + Coordinates of R : (0, 3 cm, 7 cm)",
        "output": "0.00e+00 joule\nExplanation: The work done in moving a charge between two points is given by the formula W = q1 * q2 * (Vp - Vq), where q1 and q2 are the charges, and Vp and Vq are the potentials at the respective points. The potential difference (Vp - Vq) is calculated as 0.009 * (1 / p - 1 / q). Plugging in the values, we get W = 0.00e+00 joule."
    },
    {
        "instruction": "Which of the following is the most precise device for measuring length: (a) a vernier callipers with 830 divisions on the sliding scale, (b) a screw guage of pitch 1 mm and 2946 divisions on the circular scale, (c) an optical instrument that can measure length to within a wavelength of light?\n",
        "input": "",
        "output": "(b)\nTo determine the most precise device for measuring length among the options given, we need to consider the number of divisions or increments on each device and the accuracy of the measurements they can provide, (a) Vernier Callipers: A vernier callipers typically consists of a main scale and a sliding scale with a vernier scale. The vernier scale allows for more precise measurements by providing additional divisions that correspond to a fraction of the main scale division. The precision of the vernier callipers depends on the number of divisions on the sliding scale. (b) Screw Gauge: A screw gauge measures small lengths based on the rotation of a screw with a known pitch. The pitch represents the distance moved per revolution of the screw. The precision of the screw gauge depends on the number of divisions on the circular scale. (c) Optical Instrument: An optical instrument that can measure length to within a wavelength of light has the potential for extremely high precision. The wavelength of light is typically in the order of nanometers, which allows for very accurate measurements. Comparing the options, the optical instrument that can measure length to within a wavelength of light offers the highest precision among the given choices. It can provide measurements with accuracy down to the scale of the wavelength of light."
    },
    {
        "instruction": "A double convex lens has radii of curvatures 9 cm and 89 cm, and is made of material with a refractive index of 1.56. What is the focal length of the lens?",
        "input": "Formula: f = 1 / ((mu - 1) * ((1 / r1) - (1 / r2)))",
        "output": "To find the focal length of the double convex lens, we use the formula f = 1 / ((mu - 1) * ((1 / r1) - (1 / r2))), where f is the focal length, mu is the refractive index of the lens material, r1 is the radius of curvature of the first surface, and r2 is the radius of curvature of the second surface. By substituting the given values into the formula, we can solve for f. In this case, the focal length of the lens is 14.6 cm., this is the final The focal length of the lens is 14.6 cm."
    },
    {
        "instruction": "A body is dropped from the top of a building of height 3984 m with an initial velocity of 174 m/s under gravity. After what time does it reach the ground?",
        "input": "height (h) = 3984 m, initial velocity (u) = 174 m/s",
        "output": "time (t) = (-(2 * initial velocity (u)) + \u221a((4 * initial velocity (u)\u00b2) + (8 * acceleration (a) * height (s)))) / (2 * acceleration (a))\nt = (-(2 * 174) + \u221a((4 * 174\u00b2) + (8 * 9.8 * 3984))) / (2 * 9.8)\nt = (-(2 * 174) + \u221a(121104 + 312345.60000000003)) / 19.6\nt = (-(2 * 174) + \u221a(433449.60000000003)) / 19.6\nt = (-(2 * 174) + \u221a(433449.60000000003)) / 19.6\nt = (-(2 * 174) + \u221a(433449.60000000003)) / 19.6\nt = (-(2 * 174) + \u221a(433449.60000000003)) / 19.6\nt = (-(2 * 174) + \u221a(433449.60000000003)) / 19.6\nt = (-(2 * 174) + \u221a(433449.60000000003)) / 19.6\nt = (-(2 * 174) + \u221a(433449.60000000003)) / 19.6\nt = (-(2 * 174) + \u221a(433449.60000000003)) / 19.6\nt = 15.8"
    },
    {
        "instruction": "What is the gravitational potential at a point P at a distance of 214 m from the center of the spherical shell of radius 288 m and mass 345 kg?",
        "input": "Gravitational Potential (V) = cal1(345, 214, 288) joule/kg",
        "output": "The gravitational potential at a point P at a distance of 214 m from the center of the spherical shell of radius 288 m and mass 345 kg is given by the formula V = (-G * m) / R, where G is the gravitational constant, m is the mass, and R is the distance. Plugging in the values, we get V = -7.99e-11 joule/kg."
    },
    {
        "instruction": "A circular coil of 29 turns and radius 12 cm carrying a current of 45 A rests with its plane normal to an external field of magnitude 0.92 T. The coil is free to turn about an axis in its plane perpendicular to the field direction. When the coil is turned slightly and released, it oscillates about its stable equilibrium with a frequency of 10 sec-1. What is the moment of inertia of the coil about its axis of rotation?",
        "input": "(m * b) / (4 * pi^2 * v^2)",
        "output": "The moment of inertia of the coil about its axis of rotation can be calculated using the formula (m * b) / (4 * pi^2 * v^2), where 'm' is the mass of the coil given by n * i * pi * r^2, 'b' is the magnitude of the external magnetic field, 'v' is the frequency of oscillation. Substituting the given values, we have (59.03680914625939 * 0.92) / (4 * 3.141592653589793^2 * 10^2) = 0.013757862576681325 kgm^2."
    },
    {
        "instruction": "Suppose that the electric field amplitude of an electromagnetic wave is E0 = 1009 N/C and that its frequency is v = 101 MHz. Determine wavelength?",
        "input": "v = 101 MHz",
        "output": "2.97 m\n\nThe wavelength can be calculated by dividing the speed of light by the frequency."
    },
    {
        "instruction": "Two heavy spheres each of mass 71 kg, 88 kg respectively are placed 107 m apart on a horizontal table. What is the gravitational potential at the mid point of the line joining the centres of the spheres? G = 6.67 x 10^-11",
        "input": "Gravitational Potential (V) = -1.98e-10 joule/kg",
        "output": "The gravitational potential at the mid point of the line joining the centres of the spheres is given by the formula V = (-1 * G * m1 / R) - (G * m2 / R), where G is the gravitational constant, m1 and m2 are the masses of the spheres, and R is the distance between them. Plugging in the values, we get V = -1.98e-10 J/kg."
    },
    {
        "instruction": "Torque of 151 Nm is transmitted to an engine at a power of 644 W. What is the angular speed of the rotor?",
        "input": "Angular Speed = Power / Torque",
        "output": "Angular Speed = 644 W / 151 Nm\n\nTo calculate the angular speed of the rotor, we use the following formula:\n\nAngular Speed = Power / Torque\n\nSubstituting the values:\n\nPower = 644 W\nTorque = 151 Nm\n\nWe find that the angular speed of the rotor is 4.3 rad/s."
    },
    {
        "instruction": "Two objects of masses 11 g and 13 g are moving along the same line and direction with velocities of 12 m/s and 11 m/s respectively. They collide and after the collision, the second object moves at a velocity of 26 m/s. Determine the initial velocity of the second object.",
        "input": "u2 = ((m1 * v1) + (m2 * v2) - (m1 * u1)) / m2",
        "output": "To find the initial velocity of the second object (u2), we use the formula:\n\nu2 = ((m1 * v1) + (m2 * v2) - (m1 * u1)) / m2\n\nSubstituting the given values, we have:\n\nu2 = ((11 * 26) + (13 * 1) - (11 * 12)) / 13\n\nSimplifying the expression gives us u2 = 12.8 m/s."
    },
    {
        "instruction": "16 identical hollow cylindrical columns of mild steel support a big structure of mass 34920 kg. The inner and outer radii of each column are 10 cm and 24 cm respectively. Calculate the compressional strain of each column.",
        "input": "strain = F / (A * Y)",
        "output": "The compressional strain of each column is 7.2e-07."
    },
    {
        "instruction": "In a meter bridge, the balance point is found to be at 951 mm from end A, when the resistor Y is of 527 ohm. Determine the resistance of X.",
        "input": "Resistance of X = ((1000 - balance_point) / balance_point) * R1",
        "output": "27.2 ohm\n\nExplanation: The resistance of X in the meter bridge can be calculated using the formula: Resistance of X = ((1000 - balance_point) / balance_point) * R1."
    },
    {
        "instruction": "Two discs of moments of inertia 8 and 35 about their respective axes, and rotating with angular speed 22 rad/s and 18 rad/s are brought into contact face to face with their axes of rotation coincident. What is the angular speed of the two-disc system?",
        "input": "Angular Speed = ((i1 * w1) + (i2 * w2)) / (i1 + i2)\nLoss in Kinetic Energy = k1 + k2 - k\n\nk1 = 0.5 * i1 * w1^2\nk2 = 0.5 * i2 * w2^2\nk = 0.5 * (i1 + i2) * w^2",
        "output": "To calculate the angular speed and loss in kinetic energy, we use the following formulas:\n\nAngular Speed = ((i1 * w1) + (i2 * w2)) / (i1 + i2)\nLoss in Kinetic Energy = k1 + k2 - k\n\nWhere,\n- i1 = Moment of inertia of the first disc\n- i2 = Moment of inertia of the second disc\n- w1 = Angular speed of the first disc\n- w2 = Angular speed of the second disc\n\nSubstituting the given values into the formulas, we find that the angular speed of the two-disc system is approximately 18.7 rad/s rad/s"
    },
    {
        "instruction": "A bike starting with an initial velocity of 825 m/s travels on a straight road at a constant rate of 87 m/s\u00b2 for 5 s. How far does the bike travel during this time?",
        "input": "initial velocity (u) = 825 m/s, acceleration (a) = 87 m/s\u00b2, time (t) = 5 s",
        "output": "5212.5 m \n\ndistance (s) = initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)\u00b2\ns = 825 * 5 + 0.5 * 87 * 5\u00b2\ns = 4125 + 1087.5\ns = 5212.5"
    },
    {
        "instruction": "The water pressure at the bottom of the trench is about 5655 x 10^4 Pa. A steel ball of initial volume 239 dm^3 is dropped into the ocean and falls to the bottom of the trench. What is the change in the volume of the ball when it reaches the bottom?",
        "input": "volume_change = (pressure * 10 * initial_volume) / (1.6 * 10^11)",
        "output": "The change in volume of the steel ball when it reaches the bottom of the trench is approximately 8.4e-05 m^3. We can calculate the volume change using the formula:\n\nvolume_change = (pressure * 10 * initial_volume) / (1.6 * 10^11)"
    },
    {
        "instruction": "A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 7 Hz. The mass of the wire is 0.013 kg and its linear mass density is 0.133 kg m-3. What is the tension in the string?\n",
        "input": "Speed^2 = Tension*length/mass",
        "output": "2.49e-01 newton\nTo find the length of the wire, we can use the formula for the fundamental frequency of a vibrating wire:\nf = (1/2L) * sqrt(T / \u03bc)\n\nWhere f is the frequency, L is the length of the wire, T is the tension in the wire, and \u03bc is the linear mass density.\n\nWe can rearrange the formula to solve for L:\n\nL = (1/2) * sqrt(T / (f^2 * \u03bc))\n\nGiven that the frequency f is \"+str(f)+\" Hz, the mass m is \"+str(m)+\" kg, and the linear mass density \u03bc is \"+str(mu)+\" kg/m\u00b3, we need to determine the tension T in the wire.\n\nThe tension T can be calculated using the formula:\n\nT = \u03bc * g * L\n\nWhere g is the acceleration due to gravity.\n\nSubstituting the known values into the formula, we can calculate the tension T.\n\nOnce we have the tension T, we can substitute it and the other known values into the formula for L to find the length of the wire in its fundamental mode.\n\nL = (1/2) * sqrt(T / (f^2 * \u03bc))\n\nCalculating this expression will give us the length of the wire."
    },
    {
        "instruction": "From a rifle, a bullet of mass 29 g is fired with a velocity of 959 m/s, if the recoil velocity of the rifle is 9.33 m/s, then calculate the mass of the rifle (in grams)?",
        "input": "Calculate recoil velocity, rifle mass, bullet velocity, or bullet mass",
        "output": "2980.8 g"
    },
    {
        "instruction": "A rod of mass 585 kg rotates about its end with angular speed 26 rad/s. The length of the rod is 14 m. What is the magnitude of angular momentum of the rod about its end?",
        "input": "Angular Momentum = c * m * r\u00b2 * w",
        "output": "To calculate the magnitude of the angular momentum, we use the following formula:\n\nAngular Momentum = c * m * r\u00b2 * w\n\nWhere,\n- c = Constant for the object\n- m = Mass of the object\n- r = Radius or length of the object\n- w = Angular speed of the object\n\nThe value of the constant (c) depends on the type of object being considered:\n- For a solid cylinder: c = 1/2\n- For a solid sphere: c = 2/5\n- For a hollow sphere: c = 2/3\n- For a rod: c = 1/3\n\nSubstituting the given values into the formula, we find that the magnitude of the angular momentum is approximately 993720.0 kg\u00b7m\u00b2."
    },
    {
        "instruction": "Two point charges q1 = 60 x 10^(-6)C and q2 = - 60 x 10^(-6)C are located at the points A:(0, 0, - 164 cm) and B:(0, 0, -126 cm), respectively. What are the total charge and electric dipole moment of the system?\n",
        "input": "Total charge = 0\nElectric dipole moment = q1 * d",
        "output": "The total charge of the system is 0 coulomb and the electric dipole moment is 1.74e-04 coulomb-m\n"
    },
    {
        "instruction": "Calculate the wavelength of a sound wave whose frequency is 308 hz and speed is 15708 m/s in a given medium ?\n",
        "input": "Wavelength = Speed / Frequency",
        "output": "51 m\nTo calculate the wavelength of a sound wave, we can use the formula: Wavelength = Speed / Frequency. In this case, the speed of the sound wave is 15708 m/s and the frequency is 308 Hz. Substituting these values into the formula, we can calculate the wavelength: Wavelength = 15708 m/s / 308 HzTo calculate the wavelength of a sound wave, we can use the formula: Wavelength = Speed / Frequency. In this case, the speed of the sound wave is 15708 m/s and the frequency is 308 Hz. Substituting these values into the formula, we can calculate the wavelength: Wavelength = 15708 m/s / 308 Hz"
    },
    {
        "instruction": "Suppose we employ a system of units in which the unit of mass equals 74 kg, the unit of length equals 40 m, the unit of time is 26 s, then value of 15 newton in new system\n",
        "input": "15 N = (m kg) * (l m) / (t^2 s^2)",
        "output": "3.43\nTo find the value of 15 newtons in the given system of units, we need to consider the relationships between the units of mass (kg), length (m), time (s), and force (Newton). In the new system of units, we have: 1 unit of mass = 3.43\n kg, 1 unit of length = 40 m, 1 unit of time = 26 s. To find the value of 15 newtons, we need to determine the conversion factors between the new system and the standard SI units. The force (Newton) can be expressed as: 15 N = (m kg) * (l m) / (t^2 s^2). Substituting the given values into this equation, we have: 15 N = (m * 3.43\n kg) * (l * 40 m) / (t^2 * 26 s^2). Simplifying this expression will give us the value of 15 newtons in the new system of units."
    },
    {
        "instruction": "A parallel plate capacitor made of circular plates of radius r = 165 cm has a capacitance C = 128 pF. The capacitor is connected to a 230 V ac supply with an angular frequency of 80 rad/s. What is the rms value of the conduction current?",
        "input": "I = 2.36e-06 ampere",
        "output": "2.36e-06 ampere\n\nThe rms value of the conduction current can be calculated by taking the square root of the average of the square of the current."
    },
    {
        "instruction": "An Electric motor takes 7 A current, if it consumes 965 J of energy in 48 s, then determine potential difference?",
        "input": "V = Energy / (I * t)",
        "output": "To calculate the potential difference, we use the formula V = Energy / (I * t), where Energy is the energy consumed (965 J), I is the current (7 A), and t is the time (48 s)., this is the final answer 2.9"
    },
    {
        "instruction": "A convex lens produces 44 times magnified real image of height 96.76 cm of an object placed in front of it. What is the height of the object taken?",
        "input": "Formula: ho = hi / n",
        "output": "To find the height of the object taken, we use the formula ho = hi / n, where ho is the height of the object, hi is the height of the image, and n is the magnification factor. By substituting the given values into the formula, we can solve for ho. In this case, the height of the object taken is 2.2 cm., this is the final The height of the object taken is 2.2 cm."
    },
    {
        "instruction": "Find the focal length of a convex lens whose power is 32.51 D.",
        "input": "Formula: f = 1 / P",
        "output": "To find the focal length of a convex lens, we use the formula f = 1 / P, where f is the focal length and P is the power. By substituting the given value of P into the formula, we can solve for f. In this case, the focal length is 0.0 m., this is the final 0.0"
    },
    {
        "instruction": "A rope of negligible mass is wound round a hollow cylinder of mass 69 kg and radius 86 cm. What is the angular acceleration of the hollow cylinder if the rope is pulled with a force of 72 N? Assume that there is no slipping.",
        "input": "Acceleration = Force / (k * mass * radius)",
        "output": "Acceleration = 72 N / (1 * 69 kg * 86 cm)\n\nTo calculate the angular acceleration of the hollow cylinder, we use the following formula:\n\nAcceleration = Force / (k * mass * radius)\n\nSubstituting the values:\n\nForce = 72 N\nk = 1\nMass = 69 kg\nRadius = 86 cm\n\nWe find that the angular acceleration of the hollow cylinder is approximately 1.2 rad/s\u00b2."
    },
    {
        "instruction": "A spring with K = 1619 Nm-1 is mounted on a table. A mass of 6 kg is attached to it. The mass is then pulled sideways by a distance of 28 cm and released. Assuming the spring is in the unstretched position at x = 0, with the direction from left to right as the positive x-axis, give x as a function of t when the mass is at maximum compressed position.",
        "input": "Formula: x = -displacement * cos(wt)",
        "output": "Using this formula: Formula: x = -displacement * cos(wt), this is the final answer derived: x = -28 cos(16t)"
    },
    {
        "instruction": "A 23 cm long metallic rod is rotated with an angular frequency of 155 rad s-1 about an axis normal to the rod passing through one of its ends. The other end of the rod is in contact with a circular metallic ring. A uniform magnetic field of 115 T parallel to the axis exists everywhere. Find the EMF developed between the center and the ring.\n",
        "input": "EMF = (B * l * w^2) / 2",
        "output": "3.18e+07 volt\n\n\nThe electromotive force (EMF) can be calculated using the formula EMF = (B * l * w^2) / 2, where B is the magnetic field magnitude, l is the length of the metallic rod, and w is the angular frequency of rotation in radians per second."
    },
    {
        "instruction": "A circuit consists of 17 V battery, 154 ohm resistance, then what is the time taken to produce 606 J of energy in the circuit?",
        "input": "t = (energy * R) / (V^2)",
        "output": "To calculate the time taken, we rearrange the formula t = (energy * R) / (V^2) to solve for t. Substituting the values, where energy is 606 J, R is 154 ohm, and V is 17 V, we can calculate the time., this is the final answer 322.9"
    },
    {
        "instruction": "If a gas of 2 moles at 54 m3 is isothermally changed to volume 20 m3 at 46 K, then what is the work done.\n",
        "input": "Work Done = n*R*T*ln(V2/V1)",
        "output": "759.4 joules\nTo calculate the work done during an isothermal expansion of a monoatomic gas, we can use the following equation: Work done = n * R * T * ln(V2/V1), where n is the number of moles of the gas, R is the ideal gas constant (approximately 8.314 J/(mol\u00b7K)), T is the temperature in Kelvin, V1 is the initial volume, and V2 is the final volume."
    },
    {
        "instruction": "A convex lens produces 69 times magnified real image of a 39.65 cm object placed in front of it. What is the height of the image formed by the lens?",
        "input": "Formula: hi = n * ho",
        "output": "To find the height of the image formed by the lens, we use the formula hi = n * ho, where hi is the height of the image, n is the magnification factor, and ho is the height of the object. By substituting the given values into the formula, we can solve for hi. In this case, the height of the image formed by the lens is 2735.8 cm., this is the final The height of the image formed by the lens is 2735.8 cm."
    },
    {
        "instruction": "A rod of mass 592 kg rotates about its end with angular speed 3 rad/s. The length of the rod is 36 m. What is the magnitude of angular momentum of the rod about its end?",
        "input": "Angular Momentum = c * m * r\u00b2 * w",
        "output": "To calculate the magnitude of the angular momentum, we use the following formula:\n\nAngular Momentum = c * m * r\u00b2 * w\n\nWhere,\n- c = Constant for the object\n- m = Mass of the object\n- r = Radius or length of the object\n- w = Angular speed of the object\n\nThe value of the constant (c) depends on the type of object being considered:\n- For a solid cylinder: c = 1/2\n- For a solid sphere: c = 2/5\n- For a hollow sphere: c = 2/3\n- For a rod: c = 1/3\n\nSubstituting the given values into the formula, we find that the magnitude of the angular momentum is approximately 767232.0 kg\u00b7m\u00b2."
    },
    {
        "instruction": "An object is placed at 464 cm in front of a convex lens. Image is formed at a distance of 1108 cm in front of it. Find the focal length of the lens.",
        "input": "Formula: 1/f = 1/v - 1/u for convex lens.",
        "output": "To find the focal length of the lens, we use the formula for convex lenses: 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the distance of the image from the lens, and u is the distance of the object from the lens. By substituting the given values into the formula, we can solve for f. In this case, the focal length of the lens is 798.3 cm., this is the final The focal length of the lens is 798.3 cm."
    },
    {
        "instruction": "Estimate the mean free path of a gas molecule in a cylinder containing gas at 42 atm and temperature 54 degree C. Take the radius of a gas molecule to be roughly 97 A.",
        "input": "mean_free_path = 1 / (sqrt(2) * pi * nu * (4 * r * r))",
        "output": "0.0 m\nHere, nu = (n * p) / (R * t1) = (6.022999999999999e+23 * 42 * 10^5) / (8.31 * 54 + 273) = 9.309221784298786e+26\nmean_free_path = 1 / (sqrt(2) * pi * 9.309221784298786e+26 * (4 * 97 * 10^-10 * 97 * 10^-10)) = 0.0"
    },
    {
        "instruction": "Four point charges q1 = -4 x 10^(-6) C, q2 = -3 x 10^(-6) C, q3 = 8 x 10^(-6) C, q4 = -8 x 10^(-6) C, are located at corners of square ABCD of side 6 cm. What is the force on a charge of -10 x 10^(-6) C placed at the centre of the square?\n",
        "input": "Force (F) = k * |q1 - q3| * |q2 - q4| * q_c / (d^2)",
        "output": "To calculate the force on the charge placed at the center of the square, we use the formula for electric force between two point charges:\nForce (F) = k * |q1 - q3| * |q2 - q4| * q_c / (d^2)\nwhere k is Coulomb's constant (9 * 10^9 N\u00b7m\u00b2/C\u00b2), q1, q2, q3, q4 are the charges at the corners of the square (in Coulombs), q_c is the charge placed at the center of the square (in Coulombs), and d is the side length of the square (in meters).\nGiven q1 = -4 x 10^(-6) C, q2 = -3 x 10^(-6) C, q3 = 8 x 10^(-6) C, q4 = -8 x 10^(-6) C, d = 6 cm, and q_c = -10 x 10^(-6) C:\nForce (F) = -3.25e+02 N\n"
    },
    {
        "instruction": "Estimate the fraction of molecular volume to the actual volume occupied by a gas at STP. Take the diameter of the gas molecule to be 630.2 A and volume occupied by a gas at STP as 22.4 L.",
        "input": "(4 * pi * d * d * d * 1000 * n) / (3 * 8 * 22.4)",
        "output": "3.5236978678679136e+33 \n (4 * pi * d * d * d * 1000 * n) / (3 * 8 * 22.4)"
    },
    {
        "instruction": "A steam engine delivers 296 J of work per minute and services 301 J of heat per minute from its boiler. How much heat is wasted per minute?\n",
        "input": "Efficiency = Work per minute/Heat per minute from its boiler, Heat Wasted = Heat per minute - (Efficiency/100)*Heat per minute",
        "output": "5 joules\nThe efficiency of an engine can be calculated using the formula: Efficiency = (Work output / Heat input) * 100"
    },
    {
        "instruction": "A convex lens produces a real image of height 560 cm of a real object of height 182 cm placed in front of it. What is the magnification of the lens?",
        "input": "Formula: m = hi / ho",
        "output": "To calculate the magnification of the lens, we use the formula m = hi / ho, where m is the magnification, hi is the height of the image, and ho is the height of the object. By substituting the given values into the formula, we can solve for m. In this case, the magnification of the lens is 3.1., this is the final The magnification of the lens is 3.1."
    },
    {
        "instruction": "A large steel wheel is to be fitted onto a shaft of the same material. At 22 degree C, the outer diameter of the shaft is 60 cm and the diameter of the central hole in the wheel is 59.982 cm. The shaft is cooled using 'dry ice'. At what temperature of the shaft does the wheel slip on the shaft? Assume the coefficient of linear expansion of the steel to be constant over the required temperature range \u03b1steel = 1.20 x 10-5K-1.",
        "input": "Required temperature = t1 + ((d2 - d1) / (\u03b1 * d1))",
        "output": "To calculate the required temperature, we use the following formula:\n\nRequired temperature = t1 + ((d2 - d1) / (\u03b1 * d1))\n\nSubstituting the given values into the formula, we find that the temperature is approximately -3.0 degree C."
    },
    {
        "instruction": "A helicopter of mass 1586 kg rises with a vertical acceleration of 11 m/s^2. The crew and the passengers weigh 378 kg. Give the magnitude and direction of",
        "input": "action of the rotor of the helicopter on surrounding air",
        "output": "41244 newton, vertically downwards\n\nThe action of the rotor of the helicopter on surrounding air can be calculated based on the given mass (1586 kg), weight of crew and passengers (378 kg), and acceleration (11 m/s^2)."
    },
    {
        "instruction": "Calculate the energy of each of the photons which correspond to light of frequency 252541 Hz. (h = 6.6 * 10^-34 Js)\n",
        "input": "E = 6.6*10^-34 * frequency",
        "output": "1.67e-28joules\nTo calculate the energy of a photon, you can use the formula: E = h * f, where E is the energy of the photon, h is the Planck constant (approximately 6.626 x 10^-34 J\u00b7s), and f is the frequency of the light."
    },
    {
        "instruction": "A toroid has a core of inner radius 149 cm and outer radius 152 cm, around which 139 turns of a wire are wound. If the current in the wire is 9 A, what is the magnetic field inside the core of the solenoid.",
        "input": "Magnetic field = (mu * n * i) / l",
        "output": "To calculate the magnetic field inside the toroid, we use the following formula:\n\nMagnetic field = (mu * n * i) / l\n\nWhere,\n- n = Number of turns of the wire\n- i = Current in the wire\n- l = Length of the wire\n\nWe calculate the length of the wire using the formula:\n- Length of the wire = (r1 + r2) * pi\n\nSubstituting the given values and evaluating the formula, we find that the magnetic field inside the core of the toroid is approximately 1.66e-04 tesla."
    },
    {
        "instruction": "A refrigerator is to maintain eatables kept inside at -60 degree C, if room temperature is 92 degree C. Calculate the coefficient of performance.\n",
        "input": "Coefficient of performance = T2/T1-T2",
        "output": "1.4\nThis formula is only applicable if the refrigerator is based on the Carnot Cycle."
    },
    {
        "instruction": "About 77 percent of the power of a 85 W light bulb is converted to visible radiation. What is the average intensity of the visible radiation at a distance of 195 m from the bulb?\n",
        "input": "Average Intensity = (Percentage Power / Total Power) / (4 * pi * distance^2)",
        "output": "1.90e-04 watt/m2\n\n\nThe average intensity of the visible radiation at a distance 'd' from the bulb can be calculated using the formula Average Intensity = (Percentage Power / Total Power) / (4 * pi * distance^2), where Percentage Power is the percentage of power converted to visible radiation, Total Power is the total power of the light bulb, and 'd' is the distance from the bulb."
    },
    {
        "instruction": "The equilibrium constant for a reaction is 615. Calculate the value of \u0394G^o, given T = 346.7.\n",
        "input": "\u0394G^o = -2.303RTlogK or -RTlnK",
        "output": "-42557.0\nTo calculate the standard Gibbs free energy change (\u0394G^o) for a reaction given the equilibrium constant (K), gas constant (R), and temperature (T), we can use the following equation: \u0394G^o = -R * T * ln(K) where ln represents the natural logarithm."
    },
    {
        "instruction": "A photon of energy 1860 eV strikes on metal surface ; the work function of the metal being 1058 eV. Calculate the kinetic energy of the emission and the velocity of the photoelectron. (Given 1 eV = 1.6020 \u00d7 10-19 J).\n",
        "input": "Kinetic Energy = Energy of Photon - Work Function of Metal",
        "output": "kinetic energy of ejected photoelectron = energy of photon - workfunction = 1860 - 1058 = 802 joules and if m is mass of ejected electron then velocity of ejected photo electron = sq.root((ke x 2)/m) = sq.root((802 x 2)/9.1e-31) = 1.68e+07 m/s\nTo calculate the kinetic energy of the emitted photoelectron and its velocity, we need to apply the principle of conservation of energy. The energy of the incident photon is used to overcome the work function of the metal and provide kinetic energy to the emitted electron.v = sqrt((2 * Kinetic energy) / m), Substituting the calculated kinetic energy and the electron mass into the equation will give us the velocity of the photoelectron."
    },
    {
        "instruction": "What is the gravitational field at the centre of the uniform solid sphere of radius 236 m and mass 113 kg?",
        "input": "Gravitational Field (g) = cal3(113, 236) N/kg",
        "output": "The gravitational field at the specified point is zero."
    },
    {
        "instruction": "If a monoatomic gas of 4 moles at 33 pas is isothermally changed to pressure 32 pas at 29 K, then what is the work done.\n",
        "input": "Work Done = n*R*T*ln(P1/P2)",
        "output": "-29.7 joules\nTo calculate the work done during an isothermal expansion of a monoatomic gas, we can use the following equation: Work done = n * R * T * ln(P1/P2), where n is the number of moles of the gas, R is the ideal gas constant (approximately 8.314 J/(mol\u00b7K)), T is the temperature in Kelvin, P1 is the initial pressure, and P2 is the final pressure."
    },
    {
        "instruction": "Current in a circuit falls from 118 A to 4 A in 0.13 s. If an average emf of 270 V induced, give an estimate of the self-inductance of the circuit.\n",
        "input": "Self-Inductance = (Average EMF * Time) / (Initial Current - Final Current)",
        "output": "3.08e-01 henry\n\n\nThe self-inductance of the circuit can be estimated using the formula Self-Inductance = (Average EMF * Time) / (Initial Current - Final Current), where Average EMF is the average induced electromotive force, Time is the time taken for the current to change, Initial Current is the initial current in the circuit, and Final Current is the final current in the circuit."
    },
    {
        "instruction": "A rope of negligible mass is wound round a solid cylinder of mass 45 kg and radius 24 cm. What is the linear acceleration of the solid cylinder if the rope is pulled with a force of 30 N? Assume that there is no slipping.",
        "input": "Acceleration = Force / (k * mass * radius)",
        "output": "Acceleration = 30 N / (0.5 * 45 kg * 24 cm)\n\nTo calculate the linear acceleration of the solid cylinder, we use the following formula:\n\nAcceleration = Force / (k * mass * radius)\n\nSubstituting the values:\n\nForce = 30 N\nk = 0.5\nMass = 45 kg\nRadius = 24 cm\n\nWe find that the linear acceleration of the solid cylinder is approximately 1.3 m/s\u00b2."
    },
    {
        "instruction": "Two heavy spheres each of mass 161 kg, 195 kg respectively are placed 113 m apart on a horizontal table. What is the gravitational potential at the mid point of the line joining the centres of the spheres? G = 6.67 x 10^-11",
        "input": "Gravitational Potential (V) = -4.20e-10 joule/kg",
        "output": "The gravitational potential at the mid point of the line joining the centres of the spheres is given by the formula V = (-1 * G * m1 / R) - (G * m2 / R), where G is the gravitational constant, m1 and m2 are the masses of the spheres, and R is the distance between them. Plugging in the values, we get V = -4.20e-10 J/kg."
    },
    {
        "instruction": "You are riding an automobile of mass 3940 kg. The suspension sags 188 cm when the entire automobile is placed on it. Also, the amplitude of oscillation decreases by 88 percent during one complete oscillation. Estimate the value of the damping constant b for the spring and shock absorber system of one wheel",
        "input": "",
        "output": "To estimate the value of the damping constant b, we first calculate the spring constant k using the formula (m * g) / (0.04 * x), where m is the mass of the automobile (3940 kg), g is the acceleration due to gravity (10 m/s^2), and x is the sag of the suspension (188 cm). Then, we use the formula (2 * m * ln(2) * log(10)) / (t), where m is the mass of the automobile (3940 kg) and t is the period of oscillation., this is the final answer: 1.00e+03 kgs-1"
    },
    {
        "instruction": "A force of 24 +/- 9 N is applied over an area of 1.78 +/- 0.03 m2. Calculate the pressure exerted over the area.\n",
        "input": "Pressure = Force/Area",
        "output": "13.48+/-5.28\nTo calculate the pressure exerted over an area, we use the formula: Pressure = Force / Area. In this case, the force applied is 24 N, and the area is 1.78 m\u00b2. The error in the force measurement is 9 N, and the error in the area measurement is 0.03 m\u00b2. To determine the error in the pressure calculation, we can use error propagation. The formula for calculating the maximum error in a function involving measured quantities is: Max Error = |dP/dx| * \u0394x, where Max Error is the maximum error, dP/dx is the derivative of the function with respect to the measured quantity (force or area), and \u0394x is the error in the measured quantity. Taking the derivative of the pressure formula with respect to force and area, we have: dP/dF = 1 / A, dP/dA = -F / A\u00b2. Substituting the given values into the error propagation formula, we can calculate the maximum error in the pressure: Max Error = |(1 / A_val) * F_error| + |(-F_val / A_val\u00b2) * A_error|. Now, we can substitute the given values to calculate the pressure and its maximum error over the given area."
    },
    {
        "instruction": "On a long horizontally moving belt, a child runs to and fro with a speed of 14 ms-1 (with respect to the belt) between his parents located 642 m apart on the moving belt. The belt moves with a speed of 8 ms-1. For an observer on a stationary platform outside, what is the speed of the child running in the direction of motion of the belt?",
        "input": "speed_child = speed_belt + speed_relative",
        "output": "The speed of the child running in the direction of motion of the belt is 22 ms-1."
    },
    {
        "instruction": "A long straight wire in the horizontal plane carries a current of of 425 A in west to east direction. What is the magnitude and direction of the magnetic field B at a point 1494 cm south of the wire.\n",
        "input": "B = (mu * i) / (2 * pi * r)",
        "output": "To calculate the magnitude and direction of the magnetic field B, we use the following formula:\n\nB = (mu * i) / (2 * pi * r)\n\nWhere,\n- B = Magnetic field\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- i = Current flowing through the wire\n- r = Distance from the wire\n\nSubstituting the given values into the formula, we find that the magnitude and direction of the magnetic field B is approximately 5.7e-06 tesla vertically downwards\n."
    },
    {
        "instruction": "What are the components of a vector (88) i + (4) j along the direction of (-1) i + (8) j?",
        "input": "component = (88 * -1 + 4 * 8) / sqrt(-1^2 + 8^2)",
        "output": "The component is -6.9 units."
    },
    {
        "instruction": "If an artificial satellite moving with a speed of 551 m/s in a circular orbit of radius 1574 m, calculate the time taken by it to complete a rotation?",
        "input": "r = 1574 m, v = 551 m/s",
        "output": "The time taken to complete a rotation is 17.9 s."
    },
    {
        "instruction": "At t = 0, a wheel is rotating with an angular velocity of 333 rad/s at a constant angular acceleration. It attains an angular velocity of 663 rad/s in t = 7 sec. What is the value of the angular acceleration?",
        "input": "angular_acceleration = (final_angular_velocity - initial_angular_velocity) / time",
        "output": "To calculate the angular acceleration, we use the following formula:\n\nangular_acceleration = (final_angular_velocity - initial_angular_velocity) / time\n\nSubstituting the given values into the formula, we find that the angular acceleration is approximately 47.1 rad/s\u00b2."
    },
    {
        "instruction": "A closely wounded solenoid of 480 turns and an area of cross-section 0.0131 m\u00b2 carries a current of 88 A. What is its associated magnetic moment?",
        "input": "n * i * A",
        "output": "The magnetic moment (m) of a solenoid is given by the formula m = n * i * A, where 'n' is the number of turns, 'i' is the current, and 'A' is the area of cross-section. Substituting the given values, we have m = 480 * 88 * 0.0131 = 553.344."
    },
    {
        "instruction": "A polythene is rubbed with wool is found to have a negative charge of 667753 x 10^(-12) C. Is there a transfer of mass from wool to polythene?\n",
        "input": "Mass = (number of electrons) * (mass of one electron)",
        "output": "To determine if there is a transfer of mass, we consider the mass associated with the number of electrons transferred:\nMass = (number of electrons) * (mass of one electron)\nGiven number of electrons = 4.173e+12, mass of one electron = 9.1 x 10^(-31) kg,\nMass = 3.798e-18 kg of mass is transferred\n"
    },
    {
        "instruction": "The number of silicon atoms per m3 is 5 x 10^28. This is doped simultaneously with 15 x 10^(22) atoms per m3 of Arsenic and 5 x 10^20 atoms per m3 of Indium. Given that the ni = 1396 x 10^16 m^(-3), calculate the number of electrons, is it p-type or n-type?\n",
        "input": "Ne = Ni + N2 + N3",
        "output": "1.50e+23, n-type semiconductor\nThe total number of electrons (Ne) is the sum of the intrinsic electrons (Ni) and the electrons contributed by the dopants.\n As the major dopant is Arsenic, it is a n-type semiconductor"
    },
    {
        "instruction": "If a car has an initial velocity of 667 m/s and has a constant acceleration of 39 m/s\u00b2 for 37 s, then what is the final velocity of the car?",
        "input": "final_velocity = initial_velocity + (acceleration * time)",
        "output": "The final velocity of the car is 2110 m/s."
    },
    {
        "instruction": "In a chamber, a uniform magnetic field of 0.0109 T is maintained. An electron is shot into the field with a speed of 96000000 m/s, making an angle of 62 degrees with the field. Determine the radius of the circular path of the electron.",
        "input": "Radius = (m * v) / (b * e * sin(d))",
        "output": "To calculate the radius of the circular path, we use the following formula:\n\nRadius = (m * v) / (b * e * sin(d))\n\nWhere,\n- m = Mass of the electron\n- v = Speed of the electron\n- b = Magnetic field\n- e = Charge of the electron\n- d = Angle between the velocity vector and the magnetic field vector\n\nWe substitute the given values into the formula and evaluate it to find that the radius of the circular path of the electron is approximately 5.67e-02 m."
    },
    {
        "instruction": "A large steel wheel is to be fitted onto a shaft of the same material. At 143 degree C, the outer diameter of the shaft is 172 cm and the diameter of the central hole in the wheel is 171.982 cm. The shaft is cooled using 'dry ice'. At what temperature of the shaft does the wheel slip on the shaft? Assume the coefficient of linear expansion of the steel to be constant over the required temperature range \u03b1steel = 1.20 x 10-5K-1.",
        "input": "Required temperature = t1 + ((d2 - d1) / (\u03b1 * d1))",
        "output": "To calculate the required temperature, we use the following formula:\n\nRequired temperature = t1 + ((d2 - d1) / (\u03b1 * d1))\n\nSubstituting the given values into the formula, we find that the temperature is approximately 136.8 degree C."
    },
    {
        "instruction": "A copper block of mass 2596 g is heated in a furnace to a temperature of 505 degree C and then placed on a large ice block. What is the maximum amount of ice that can melt? Specific heat of copper is 0.39 Jg-1\u00b0C-1. Heat of fusion of water = 335 Jg-1.",
        "input": "Maximum amount of ice melted = (mass of block * temperature change * specific heat) / heat of fusion of water",
        "output": "To calculate the maximum amount of ice melted, we use the following formula:\n\nMaximum amount of ice melted = (mass of block * temperature change * specific heat) / heat of fusion of water\n\nSubstituting the given values into the formula, we find that the maximum amount of ice that can melt is approximately 1526.2 g."
    },
    {
        "instruction": "A body describes simple harmonic motion with an amplitude of 30 mm and a period of 56 ms. Find the acceleration of the body when the displacement is 2 mm?\n",
        "input": "w*w*amp",
        "output": "Using this formula: w*w*amp, this is the final answer derived: 2.52e+04 ms-2\n"
    },
    {
        "instruction": "A body is dropped with an initial velocity of 270 m/s and reaches the ground with a velocity of 311 m/s. From what height was it dropped?",
        "input": "initial velocity (u) = 270 m/s, final velocity (v) = 311 m/s",
        "output": "height (h) = (final velocity (v)\u00b2 - initial velocity (u)\u00b2) / (2 * acceleration (g))\nh = (311\u00b2 - 270\u00b2) / (2 * 9.8)\nh = (96721 - 72900) / 19.6\nh = 1215.4"
    },
    {
        "instruction": "A trolley of mass 35 kg moves with a uniform speed of 16 m/s on a frictionless track. A child of mass 13 kg runs on the trolley from one end to the other (10 m away) with a speed of 2 m/s relative to the trolley in a direction opposite to the trolley\u2019s motion, and jumps out of the trolley. How much has the trolley moved from the time the child begins to run?",
        "input": "distance = (m2 * v2) / (m1 + m2) + v1 * time",
        "output": "Using the formula: distance = (m2 * v2) / (m1 + m2) + v1 * time, the final answer is: {'answer': '82.5 m', 'explanation': 'To find the distance covered by the trolley from the time the child begins to run, we need to calculate the time it takes for the child to reach the other end of the trolley. The time can be found by dividing the distance by the relative velocity between the trolley and the child. Once we have the time, we can multiply it by the velocity of the trolley to find the distance covered. Therefore, the trolley has moved 82.5 m m from the time the child begins to run.'}"
    },
    {
        "instruction": "A hollow cylinder of radius 132 m weighs 63 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 2 m/s. How much work has to be done to stop it?\n",
        "input": "0.5*(1+1)*m*v*v",
        "output": "252.0 joules\n"
    },
    {
        "instruction": "An aircraft of mass 108 kg executes a horizontal loop at a speed of 49 m/s with its wings banked at 59 degrees. What is the radius of the loop?",
        "input": "(v^2) / (g * tan((param * pi) / 180))",
        "output": "144\nTo calculate the radius, we use the formula (v^2) / (g * tan((param * pi) / 180)), where v is the speed (49 m/s), g is the acceleration due to gravity (10 m/s^2), and param is the angle of banking (59 degrees)."
    },
    {
        "instruction": "If in a space electric field is along z-axis, increases uniformly along +ve z-direction, at the rate of 65100 NC\u207b\u00b9 per meter. What are the values of force and torque experienced by a system having a total dipole moment of 1863 x 10\u207b\u2079 Cm in the negative z-direction?\n",
        "input": "Force = Electric field * Dipole moment",
        "output": "To calculate the force and torque experienced by the system, we need to consider the interaction between the electric field and the dipole moment:\nForce = Electric field * Dipole moment\nTorque = 0\nGiven electric field rate = 65100 NC\u207b\u00b9/m, dipole moment = 1863 x 10\u207b\u2079 Cm:\nForce = 1.21e-01 N\n"
    },
    {
        "instruction": "A small bulb is placed at the bottom of a tank containing liquid to a depth of 238 cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of the liquid is 1.19.",
        "input": "Formula: Area = \u03c0 * h\u00b2 * (k / (1 - k)), where h is the depth of the liquid in centimeters, and k is the reciprocal of the refractive index of the liquid.",
        "output": "This is the answer 42.77 m\u00b2, formula used is : Formula: Area = \u03c0 * h\u00b2 * (k / (1 - k)), where h is the depth of the liquid in centimeters, and k is the reciprocal of the refractive index of the liquid."
    },
    {
        "instruction": "Calculate the wavelength of a sound wave whose frequency is 503 hz and speed is 133798 m/s in a given medium ?\n",
        "input": "Wavelength = Speed / Frequency",
        "output": "266 m\nTo calculate the wavelength of a sound wave, we can use the formula: Wavelength = Speed / Frequency. In this case, the speed of the sound wave is 133798 m/s and the frequency is 503 Hz. Substituting these values into the formula, we can calculate the wavelength: Wavelength = 133798 m/s / 503 HzTo calculate the wavelength of a sound wave, we can use the formula: Wavelength = Speed / Frequency. In this case, the speed of the sound wave is 133798 m/s and the frequency is 503 Hz. Substituting these values into the formula, we can calculate the wavelength: Wavelength = 133798 m/s / 503 Hz"
    },
    {
        "instruction": "An Electric bulb of resistance 16 ohm produces heat at 80 W for 613 s. Calculate the potential difference maintained at service mains?",
        "input": "V = sqrt(P * R)",
        "output": "35.8 volt\n\nThe potential difference maintained at service mains can be calculated using the formula: V = sqrt(P * R), where P is the power and R is the resistance."
    },
    {
        "instruction": "The radius of a sphere is measured as 610.1 +/- 23.7 cm calculate its surface area (in m2) with error limits.\n",
        "input": "Surface Area = 4\u03c0r\u00b2",
        "output": "467.5+/-36.3\nTo calculate the surface area of a sphere with a measured radius, we use the formula: Surface Area = 4\u03c0r\u00b2. In this case, the radius of the sphere is 610.1 cm, and the error in the measurement is 36.3 cm. To determine the error in the surface area calculation, we can use error propagation. The formula for calculating the maximum error in a function involving measured quantities is: Max Error = |dA/dx| * \u0394x, where Max Error is the maximum error, dA/dx is the derivative of the function with respect to the measured quantity (radius in this case), and \u0394x is the error in the measured quantity. Taking the derivative of the surface area formula with respect to the radius, we have: dA/dr = 8\u03c0r. Substituting the given values into the error propagation formula, we can calculate the maximum error in the surface area: Max Error = |8\u03c0r| * \u0394r. Now, we can substitute the given radius and error values to calculate the maximum error in the surface area."
    },
    {
        "instruction": "A sound produces 449 crests and 449 troughs in 19 seconds. When the first trough is produced, the first crest is 1265 m away from the source, then calculate the wavelength ?\n",
        "input": "Wavelength = Speed*Time Period, ",
        "output": "2530 m\nTo calculate the speed of sound, we need to determine the distance traveled by a crest or trough in the given time interval. In 19 seconds, 449 crests and 449 troughs are produced. This means that one complete cycle of the wave (a crest and a trough) occurs 449 times in 19 seconds. Therefore, the time taken for one complete cycle (T) can be calculated as: T = 19 s / 449 cycles. The distance traveled by one complete cycle (wavelength, \u03bb) is given by the formula: \u03bb = speed * T, where speed is the speed of sound. Since the first crest is 1265 m away from the source, the distance traveled by a complete cycle (\u03bb) can be expressed as: \u03bb = 1265 m + 1265 m = 2 * 1265 m. Substituting the value of \u03bb and T into the equation, we can calculate the speed of sound: speed = \u03bb / T = (2 * 1265 m) / (19 s / 449 cycles). Calculating this expression will give us the speed of sound."
    },
    {
        "instruction": "If a diatomic gas of 7 moles at 167 atm and volume 182 lit is isothermally changed to volume 94 lit, then what will be the pressure.\n",
        "input": "P1*V1 = P2*V2",
        "output": "323.3atm\nTo determine the final pressure of a diatomic gas after an isothermal expansion, we can use Boyle's Law, which states that for an ideal gas at constant temperature: P1 * V1 = P2 * V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume."
    },
    {
        "instruction": "A convex mirror produces a real image of height 29 cm of a real object having a height of 81 cm and placed 50 cm in front of it. At what distance is the image formed from the mirror?",
        "input": "Formula: m = v / u = hi / ho",
        "output": "To find the distance of the image from the mirror, we use the formula m = v / u = hi / ho, where m is the magnification, v is the distance of the image from the mirror, u is the distance of the object from the mirror, hi is the height of the image, and ho is the height of the object. By rearranging the formula, we can calculate v as v = (u * hi) / ho. By substituting the given values into the formula, we find that the image is formed at a distance of 17.9 cm from the mirror., this is the final The image is formed at a distance of 17.9 cm from the mirror."
    },
    {
        "instruction": "Two point charges q1 = 11 x 10^(-6)C and q2 = - 11 x 10^(-6)C are located at the points A:(0, 0, - 60 cm) and B:(0, 0, -48 cm), respectively. What are the total charge and electric dipole moment of the system?\n",
        "input": "Total charge = 0\nElectric dipole moment = q1 * d",
        "output": "The total charge of the system is 0 coulomb and the electric dipole moment is 1.19e-05 coulomb-m\n"
    },
    {
        "instruction": "A force of 154 +/- 10 N is applied over an area of 0.81 +/- 0.07 m2. Calculate the pressure exerted over the area.\n",
        "input": "Pressure = Force/Area",
        "output": "190.12+/-28.78\nTo calculate the pressure exerted over an area, we use the formula: Pressure = Force / Area. In this case, the force applied is 154 N, and the area is 0.81 m\u00b2. The error in the force measurement is 10 N, and the error in the area measurement is 0.07 m\u00b2. To determine the error in the pressure calculation, we can use error propagation. The formula for calculating the maximum error in a function involving measured quantities is: Max Error = |dP/dx| * \u0394x, where Max Error is the maximum error, dP/dx is the derivative of the function with respect to the measured quantity (force or area), and \u0394x is the error in the measured quantity. Taking the derivative of the pressure formula with respect to force and area, we have: dP/dF = 1 / A, dP/dA = -F / A\u00b2. Substituting the given values into the error propagation formula, we can calculate the maximum error in the pressure: Max Error = |(1 / A_val) * F_error| + |(-F_val / A_val\u00b2) * A_error|. Now, we can substitute the given values to calculate the pressure and its maximum error over the given area."
    },
    {
        "instruction": "A hoop rolls down two different inclined planes of the same height 13 cm but with angles of inclination of 74 and 23, on which it will reach the ground faster?",
        "input": "time = sqrt((k + 1) * height) / sin(angle)",
        "output": "To compare the times, we use the following formula:\n\ntime = sqrt((k + 1) * height) / sin(angle)\n\nSubstituting the given values into the formula, we find that:\n\nThe first plane takes less time to reach the ground."
    },
    {
        "instruction": "A series LCR circuit is connected to a variable frequency 230 V source with L = 14 H, C = 74 muF, R = 46 ohm. Determine the amplitude of current at the resonating frequency?",
        "input": "Current Amplitude = V_amplitude / Impedance",
        "output": "Current Amplitude = 7.1 A"
    },
    {
        "instruction": "A truck starts from rest and accelerates uniformly at 3 ms-2. At t = 31 s, a stone is dropped by a person standing on the top of the truck (1 m high from the ground). What are the (a) velocity, and (b) acceleration of the stone at t = 55 s? (Neglect air resistance.)",
        "input": "A truck starts from rest and accelerates uniformly at 3 ms-2. At t = 31 s, a stone is dropped by a person standing on the top of the truck (1 m high from the ground). What are the (a) velocity, and (b) acceleration of the stone at t = 55 s? (Neglect air resistance.)",
        "output": "Velocity is 257.4 ms-1, at an angle of 69 degrees with horizontal. Acceleration is g (10 ms-2) downwards."
    },
    {
        "instruction": "A steel cable with a radius of 145 mm supports a chairlift at a ski area. If the maximum stress is not to exceed 31598 x 10^(6) Nm-2, what is the maximum load the cable can support?",
        "input": "",
        "output": "The maximum load the cable can support is 2.1e+03 newton."
    },
    {
        "instruction": "A circular coil of wire consisting of 173 turns, each of radius 162 cm placed in a horizontal plane carries a current of 17 A in anticlockwise direction. What is the magnitude and direction of the magnetic field B at the center of the coil?",
        "input": "B = (mu * n * i) / (2 * r)",
        "output": "To calculate the magnetic field B at the center of the coil, we use the following formula:\n\nB = (mu * n * i) / (2 * r)\n\nWhere,\n- B = Magnetic field at the center of the coil\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- n = Number of turns in the coil\n- i = Current flowing through the coil\n- r = Radius of the coil\n\nSubstituting the given values into the formula, we find that the magnitude of the magnetic field B is approximately 1.14e-03 tesla vertically upwards."
    },
    {
        "instruction": "From a rifle of mass 5200 g, a bullet is fired with a velocity of 914 m/s, if the recoil velocity of the rifle is 9.39 m/s, then calculate the mass of the bullet (in grams)?",
        "input": "Calculate recoil velocity, rifle mass, bullet velocity, or bullet mass",
        "output": "53.4 g"
    },
    {
        "instruction": "An object is projected with an initial velocity of 802 m/s. If the maximum height reached by it is 9931 m, what is the angle of projection?",
        "input": "",
        "output": "33 degrees w.r.t. to the ground"
    },
    {
        "instruction": "Two discs of moments of inertia 36 and 46 about their respective axes, and rotating with angular speed 86 rad/s and 84 rad/s are brought into contact face to face with their axes of rotation coincident. What is the loss in kinetic energy of the two-disc system?",
        "input": "Angular Speed = ((i1 * w1) + (i2 * w2)) / (i1 + i2)\nLoss in Kinetic Energy = k1 + k2 - k\n\nk1 = 0.5 * i1 * w1^2\nk2 = 0.5 * i2 * w2^2\nk = 0.5 * (i1 + i2) * w^2",
        "output": "To calculate the angular speed and loss in kinetic energy, we use the following formulas:\n\nAngular Speed = ((i1 * w1) + (i2 * w2)) / (i1 + i2)\nLoss in Kinetic Energy = k1 + k2 - k\n\nWhere,\n- i1 = Moment of inertia of the first disc\n- i2 = Moment of inertia of the second disc\n- w1 = Angular speed of the first disc\n- w2 = Angular speed of the second disc\n\nSubstituting the given values into the formulas, we find that the loss in kinetic energy is approximately 40.4 joules joules."
    },
    {
        "instruction": "The piston in the cylinder head of a locomotive has a stroke (10 times the amplitude) of 50 m. If the piston moves with SHM with an angular frequency of 981 rev/min, what its amplitude, maximum speed?\n",
        "input": "amp2 = amp/ratio, v = (freq*amp2)/60",
        "output": "amp2 = amp/ratio, v = (freq*amp2)/60  this is the final answer: amplitude is 5.00e+00 m, its maximum speed is 8.18e+01 ms-1\n"
    },
    {
        "instruction": "In a meter bridge, the balance point is found to be at 454 mm from end A, when the resistor Y is of 3031 ohm. Determine the resistance of X.",
        "input": "Resistance of X = ((1000 - balance_point) / balance_point) * R1",
        "output": "3645.2 ohm\n\nExplanation: The resistance of X in the meter bridge can be calculated using the formula: Resistance of X = ((1000 - balance_point) / balance_point) * R1."
    },
    {
        "instruction": "A vertical off-shore structure is built to withstand a maximum stress of 9800000 Pa. Is the structure suitable for putting up on top of an oil well in the ocean? Take the depth of the ocean to be roughly 10 km, and ignore ocean currents?",
        "input": "10 * 1000 * 980",
        "output": "yes, it is suitable"
    },
    {
        "instruction": "A force is applied on a body of mass 737 kg placed on a smooth surface resulting in acceleration of 575 m/s^2, then what is the force applied?",
        "input": "F = m * a",
        "output": "423775\nTo calculate the force, we use the formula F = m * a, where F is the force, m is the mass (737 kg), and a is the acceleration (575 m/s^2)."
    },
    {
        "instruction": "What is the magnitude of the magnetic force per unit length on a wire carrying a current of 149 A and making an angle of 179 degrees with the direction of a uniform magnetic field of 90 tesla?",
        "input": "Force per unit length = b * i * sin(d)",
        "output": "To calculate the magnitude of the magnetic force, we use the following formula:\n\nForce per unit length = b * i * sin(d)\n\nSubstituting the given values:\n- b = 90 tesla\n- i = 149 A\n- d = 179 degrees\n\nAfter evaluating the formula, we find that the magnetic force per unit length is approximately 234.0 newtons per meter."
    },
    {
        "instruction": "An aircraft is flying at a height of 891 m above the ground. If the angle subtended at a ground observation point by the aircraft positions 2 s apart is 72 degrees, what is the speed of the aircraft?",
        "input": "speed = (2 * h * tan(angle)) / time",
        "output": "The speed of the aircraft is 647.3 ms-1."
    },
    {
        "instruction": "A person with a hypermetropic eye cannot see objects within 29160 mm distinctly. What should be the type of the corrective lens used to restore proper vision?\n",
        "input": "1/f=1/v-1/u",
        "output": "the remedial lens should make the objects at defected eye's near point appear at normal eye's near point, hence u = 25cm, v = near point of defected eye, from P=1/f, 1/f=1/v-1/u, we get P=1/v-1/u, P=1/v-(1/-0.25)=1/v+1/0.25, implies P = 3.97 diatrope, type of lens required is convex\n"
    },
    {
        "instruction": "A series LCR circuit is connected to a variable frequency 230 V source with L = 174 H, C = 110 muF, R = 196 ohm. Determine the source frequency which drives the circuit in resonance?",
        "input": "Source Frequency = 1 / sqrt(L * C)",
        "output": "7.2 rad/s"
    },
    {
        "instruction": "A plane electromagnetic wave travels in vacuum along the z-direction. If the frequency of the wave is 190717100 Hz, what is its wavelength?",
        "input": "f = 190717100 Hz",
        "output": "1.57e+00 m\n\nThe wavelength of the wave can be calculated by dividing the speed of light by the frequency."
    },
    {
        "instruction": "A 21 watt bulb emits monochromatic yellow light of wavelength 424154 pm. Calculate the rate of emission of quanta per second.\n",
        "input": "Rate of emission per quanta = Power*wavelength/h*c",
        "output": "4.50e+19per second\nTo calculate the rate of emission of quanta per second, we need to determine the number of photons emitted per second by the light bulb.The energy of each photon can be calculated using the formula: Energy of each photon = h * c / \u03bb, where h is the Planck constant (approximately 6.626 x 10^-34 J\u00b7s), c is the speed of light (approximately 3 x 10^8 m/s), and \u03bb is the wavelength of light in meters.Now, we can calculate the rate of emission of quanta per second using the formula: Rate of emission = Power / Energy of each photon, where Power is the power of the light bulb in watts."
    },
    {
        "instruction": "A double concave lens has radii of curvatures 5 cm and 23 cm, and is made of material with a refractive index of 1.28. What is the focal length of the lens?",
        "input": "Formula: f = 1 / ((mu - 1) * ((1 / r1) - (1 / r2)))",
        "output": "To find the focal length of the double concave lens, we use the formula f = 1 / ((mu - 1) * ((1 / r1) - (1 / r2))), where f is the focal length, mu is the refractive index of the lens material, r1 is the radius of curvature of the first surface, and r2 is the radius of curvature of the second surface. By substituting the given values into the formula, we can solve for f. In this case, the focal length of the lens is -14.67 cm., this is the final The focal length of the lens is -14.67 cm."
    },
    {
        "instruction": "An image is formed by a concave mirror of focal length 641 cm at a distance of 1376 cm in front of it. Find at what distance object is placed in front of mirror.",
        "input": "Formula: 1/f = 1/v - 1/u",
        "output": "To find the distance of the object, we use the formula 1/f = 1/v - 1/u, where f is the focal length, v is the distance of the image, and u is the distance of the object. By substituting the given values into the formula, we can solve for u. In this case, the distance of the object is 1200.0 cm., this is the final 1200.0"
    },
    {
        "instruction": "A 175 ohm resistor is connected to a 235 V, 75 Hz ac supply. What is the net power consumed over a full cycle?",
        "input": "P_net = (V ** 2) / R",
        "output": "3.16e+02 watt"
    },
    {
        "instruction": "Two moving coil meters M1 and M2 have the following particulars R1 = 5 ohms, N1 = 1, A1 = 0.0007 m2 , B1 = 3 T, K1 = 2 and  R2 = 5 ohms, N2 = 1 , A1 = 0.0004 m2 , B1 = 1 T, K2 = 7. Determine the ratio of current sensitivities of M1 and M2.\n",
        "input": "Ratio of current sensitivity of M1 to M2 is given by, n1 x b1 x a1 x k2 : n2 x b2 x a2 x k1",
        "output": "Ratio of current sensitivity of M1 to M2 is given by, n1 x b1 x a1 x k2 : n2 x b2 x a2 x k1 = 1 x 3 x 0.0007 x 7 : 1 x 1 x 0.0004 x 2 = 18.4\n"
    },
    {
        "instruction": "Suppose that the electric field amplitude of an electromagnetic wave is E0 = 1935 N/C and that its frequency is v = 1054 MHz. Determine k?",
        "input": "v = 1054 MHz",
        "output": "2.21e+01 rad/m\n\nThe wave number (k) can be determined by dividing the angular frequency by the speed of light."
    },
    {
        "instruction": "What is the gravitational field at a point P at a distance of 312 m from the center of the spherical shell of radius 382 m and mass 215 kg?",
        "input": "Gravitational Field (g) = 0 N/kg",
        "output": "The gravitational field at the specified point is zero."
    },
    {
        "instruction": "If a gas of 6 moles at 36 m3 is isothermally changed to volume 34 m3 at 13 K, then what is the work done.\n",
        "input": "Work Done = n*R*T*ln(V2/V1)",
        "output": "37.0 joules\nTo calculate the work done during an isothermal expansion of a monoatomic gas, we can use the following equation: Work done = n * R * T * ln(V2/V1), where n is the number of moles of the gas, R is the ideal gas constant (approximately 8.314 J/(mol\u00b7K)), T is the temperature in Kelvin, V1 is the initial volume, and V2 is the final volume."
    },
    {
        "instruction": "Find the ratio of time taken by the sound wave to travel a distance of 2 m in material-1 and material-2 (speed of sound in material-1 is 268 m/s, in material-2 is 8754 m/s) ?\n",
        "input": "Speed = Distance/Time",
        "output": "32.7\nTo find the ratio of the time taken by the sound wave to travel a distance of 2 m in material-1 and material-2, we can use the equation: Ratio of time = time in material-1 / time in material-2. The time taken by the sound wave to travel a distance in material-1 can be calculated using the equation: time in material-1 = distance / speed in material-1. Similarly, the time taken by the sound wave to travel the same distance in material-2 can be calculated using: time in material-2 = distance / speed in material-2. Substituting the given values into the equations, we have: time in material-1 = 2 m / 268 m/, time in material-2 = 2 m / 8754 m/s. Therefore, the ratio of the time taken by the sound wave to travel a distance of 2 m in material-1 and material-2 is: Ratio of time = (2 m / 268 m/s) / (2 m / 8754 m/s)= 32.66417910447761"
    },
    {
        "instruction": "A radio can tune in to any station in the 745 kHz to 3398 kHz band. What is the corresponding wavelength band?",
        "input": "f1 = 745 kHz, f2 = 2653 kHz",
        "output": "88.29 m to 402.68 m\n\nThe corresponding wavelength band can be calculated by dividing the speed of light by the frequency range."
    },
    {
        "instruction": "A long straight wire in the horizontal plane carries a current of of 319 A in north to south direction. What is the magnitude and direction of the magnetic field B at a point 1688 cm west of the wire.\n",
        "input": "B = (mu * i) / (2 * pi * r)",
        "output": "To calculate the magnitude and direction of the magnetic field B, we use the following formula:\n\nB = (mu * i) / (2 * pi * r)\n\nWhere,\n- B = Magnetic field\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- i = Current flowing through the wire\n- r = Distance from the wire\n\nSubstituting the given values into the formula, we find that the magnitude and direction of the magnetic field B is approximately 3.8e-06 tesla vertically downwards\n."
    },
    {
        "instruction": "A convex lens produces 87 times diminished real image of a 59.25 cm object placed in front of it. What is the height of the image formed by the lens?",
        "input": "Formula: hi = ho / n",
        "output": "To find the height of the image formed by the lens, we use the formula hi = ho / n, where hi is the height of the image, ho is the height of the object, and n is the magnification factor. By substituting the given values into the formula, we can solve for hi. In this case, the height of the image formed by the lens is 0.7 cm., this is the final The height of the image formed by the lens is 0.7 cm."
    },
    {
        "instruction": "A person with a myopic eye cannot see objects beyond 77484 mm distinctly. What should be the type of the corrective lens used to restore proper vision?\n",
        "input": "1/f=1/v-1/u",
        "output": "the remedial lens should make the objects at infinity appear at far point, hence u = infinity, v = far point of defected eye, from P=1/f, 1/f=1/v-1/u, we get P=1/v-1/u, P=1/v-0=1/v, implies P = 0.01 diatrope, type of lens required is concave.\n"
    },
    {
        "instruction": "The edge of a cube is 124 cm long. One face of the cube is firmly fixed to a vertical wall. A mass of 31 kg is then attached to the opposite face of the cube. The shear modulus of the material of the cube is 56 GPa. What is the vertical deflection of this face?",
        "input": "deflection = (mass * 9.8) / (Y * 10^9 * (edge_length * 10^-2))",
        "output": "To calculate the vertical deflection, we use the formula:\n\ndeflection = (mass * 9.8) / (Y * 10^9 * (edge_length * 10^-2))\n   = (31 kg * 9.8) / (56 * 10^9 GPa * (124 cm * 10^-2 m/cm))\n   = 4.4 nm."
    },
    {
        "instruction": "Estimate the distance for which ray optics is good approximation for an aperture of 7 mm and wavelength 81 nm.\n",
        "input": "Fresnel Distance = Aperture^2/Wavelength of light",
        "output": "6.05e+08 m\nThe criterion for ray optics to be a good approximation is when the size of the aperture is much larger than the wavelength of light. This condition ensures that the wave nature of light can be neglected, and light can be treated as a ray.To estimate the distance for which ray optics is a good approximation, we can use the following formula: Distance \u2248 2 * (aperture size)^2 / (wavelength)"
    },
    {
        "instruction": "A short bar magnet of magnetic moment 18.21 J/T is placed in a uniform magnetic field of 9.05 T. If the magnet is free to rotate in the plane of the field, what is the potential energy of the magnet at stable position?",
        "input": "-m * b",
        "output": "The potential energy of the magnet at a stable position can be calculated using the formula -m * b, where 'm' is the magnetic moment of the bar magnet and 'b' is the magnetic field strength. Substituting the given values, we have -(18.21) * 9.05 = -1.65e+02 joule."
    },
    {
        "instruction": "A hoop of mass 9241 kg has a radius of 73 m. What is the moment of inertia with respect to its diameter?",
        "input": "Moment of Inertia = (Constant) * mass * radius^2",
        "output": "The moment of inertia with respect to its diameter is approximately 24622644.5 kgm^2.\n\nMoment of Inertia = (Constant) * mass * radius^2\n\nConstant = 0.5\nmass = 9241 kg\nradius = 73 m"
    },
    {
        "instruction": "A convex mirror produces a real image of height 13 cm at a distance of 10 cm from it of a real object placed 105 cm in front of it. What is the height of the object?",
        "input": "Formula: m = v / u = hi / ho",
        "output": "To find the height of the object, we use the formula m = v / u = hi / ho, where m is the magnification, v is the distance of the image from the mirror, u is the distance of the object from the mirror, hi is the height of the image, and ho is the height of the object. By rearranging the formula, we can calculate ho as ho = (hi * u) / v. By substituting the given values into the formula, we find that the height of the object is 136.5 cm., this is the final The height of the object is 136.5 cm."
    },
    {
        "instruction": "A sound wave travels at a speed of 885932.0 m/s, if it's wavelength is 38 m, will the sound wave be audible ? \n",
        "input": "frequency = wave speed / wavelength",
        "output": "not audible\nWhether a sound wave is audible or not depends on its frequency, not its wavelength. Audible sound waves have frequencies within the range of human hearing, which is typically between 20 Hz and 20,000 Hz. To determine if a sound wave is audible, we need to calculate its frequency using the wave speed and wavelength. The formula to calculate the frequency of a sound wave is: f = v / \u03bb, where f is the frequency, v is the wave speed, and \u03bb is the wavelength. Substituting the given values into the formula, we can calculate the frequency of the sound wave: f = 885932.0 m/s / 38 m. Now, we can compare the calculated frequency to the audible frequency range (20 Hz to 20,000 Hz) to determine if the sound wave is audible or not."
    },
    {
        "instruction": "In a Youngs double-slit experiment using monochromatic light of wavelength 31, the intensity of light at a point on the screen where path difference is 6.2, is 38 units. What is the intensity of light at a point where path difference is 31.0.\n",
        "input": "Phase difference = (2*pi/wavelength)*path difference, Intensity = I0*cos^2(phase difference)",
        "output": "5.81e+01 units\nIn a Young's double-slit experiment, the intensity of light at a point on the screen is directly related to the amplitude of the light waves arriving at that point. The intensity is given by the formula: I \u221d A^2, where I is the intensity and A is the amplitude of the light waves.Therefore, the intensity of light at a point where the path difference is 31.0 is 38 units, same as the intensity at the point with the path difference 6.2."
    },
    {
        "instruction": "The piston in the cylinder head of a locomotive has a stroke (2 times the amplitude) of 45 m. If the piston moves with SHM with an angular frequency of 1057 rev/min, what its amplitude, maximum speed?\n",
        "input": "amp2 = amp/ratio, v = (freq*amp2)/60",
        "output": "amp2 = amp/ratio, v = (freq*amp2)/60  this is the final answer: amplitude is 2.25e+01 m, its maximum speed is 3.96e+02 ms-1\n"
    },
    {
        "instruction": "Suppose that the electric field amplitude of an electromagnetic wave is E0 = 843 N/C and that its frequency is v = 279 MHz. Find an expression for E?",
        "input": "E0 = 843 N/C, k = 5.84e+00 rad/m, w = 1.75e+09 rad/s",
        "output": "843sin[5.84e+00x-1.75e+09t]\n\nThe expression for the electric field (E) of an electromagnetic wave can be written as E = E0sin(kx - wt)."
    },
    {
        "instruction": "A truck starts from rest and accelerates uniformly at 16 ms-2. At t = 200 s, a stone is dropped by a person standing on the top of the truck (17 m high from the ground). What are the (a) velocity, and (b) acceleration of the stone at t = 225 s? (Neglect air resistance.)",
        "input": "A truck starts from rest and accelerates uniformly at 16 ms-2. At t = 200 s, a stone is dropped by a person standing on the top of the truck (17 m high from the ground). What are the (a) velocity, and (b) acceleration of the stone at t = 225 s? (Neglect air resistance.)",
        "output": "Velocity is 3209.8 ms-1, at an angle of 4 degrees with horizontal. Acceleration is g (10 ms-2) downwards."
    },
    {
        "instruction": "A charge of 10 mC is located at the origin. Calculate the work done in taking a charge 8 nC from a point P(0, 0, 14 cm) to a point Q(0, 0, 8 cm), via a point R(0, 14 cm, 1 cm).",
        "input": "Charge at Origin (q1) = 10 mC + Charge at P (q2) 8 nC + Coordinates of P: (0, 0, 14 cm) + Coordinates of Q : (0, 0, 8 cm) + Coordinates of R : (0, 14 cm, 1 cm)",
        "output": "3.86e-02 joule\nExplanation: The work done in moving a charge between two points is given by the formula W = q1 * q2 * (Vp - Vq), where q1 and q2 are the charges, and Vp and Vq are the potentials at the respective points. The potential difference (Vp - Vq) is calculated as 0.009 * (1 / p - 1 / q). Plugging in the values, we get W = 3.86e-02 joule."
    },
    {
        "instruction": "What is the velocity of an object of mass 388 kg having kinetic energy of 498386 J?",
        "input": "v = sqrt((2 * KE) / m)",
        "output": "To calculate the velocity, we use the formula v = sqrt((2 * KE) / m), where v is the velocity, KE is the kinetic energy (498386 J), and m is the mass (388 kg)., this is the final answer 50.7"
    },
    {
        "instruction": "What is the electric field at a point P at a distance of 232 m from the center of the uniform solid sphere of radius 312 m and having -1.03e-06 C charge distributed uniformly.",
        "input": "Electric Field (E) = cal4(-1.03e-06, 232, 312) N/C",
        "output": "-7.08e-02 newton/coulomb\nThe electric field inside a uniformly charged solid sphere is given by the formula E = k * Q * r / (R^3), where k is the Coulomb's constant, Q is the charge on the sphere, r is the distance from the center, and R is the radius of the sphere. Plugging in the values, we get E = -7.08e-02 N/C."
    },
    {
        "instruction": "A piece of copper having a rectangular cross-section of 23 mm x 55 mm is pulled in tension with 70400 N force, producing only elastic deformation. Calculate the resulting strain? Shear modulus of elasticity of copper is 42 x 10^9 N/m^2.",
        "input": "strain = force / (A * (shear_modulus * 10^9))",
        "output": "To calculate the resulting strain, we use the formula:\n\nstrain = force / (A * (shear_modulus * 10^9))\n   = 70400 N / (23 mm * 55 mm * 10^-6 m^2 * (42 * 10^9 N/m^2))\n   = 1325.1 x 10^(-6)."
    },
    {
        "instruction": "What is the gravitational potential at a point P on the surface of the spherical shell of radius 203 m and mass 363 kg?",
        "input": "Gravitational Potential (V) = cal1(363, 134, 203) joule/kg",
        "output": "The gravitational potential at a point P at a distance of 134 m from the center of the spherical shell of radius 203 m and mass 363 kg is given by the formula V = (-G * m) / R, where G is the gravitational constant, m is the mass, and R is the distance. Plugging in the values, we get V = -1.19e-10 joule/kg."
    },
    {
        "instruction": "A sonar device on a submarine sends out a signal and receives an echo 647 s later. Find the speed of sound in that material if the distance of the object from the submarine is 4463 m ?\n",
        "input": "Distance = Speed * Time",
        "output": "13.8 m/s\nTo find the speed of sound in the material, we can use the equation: Speed = Distance / Time. In this case, the distance of the object from the submarine is 4463 meters and the time it takes for the echo to return is 647 seconds. Substituting these values into the equation, we can calculate the speed of sound in the material: Speed = 4463 m / 647 s. Calculating this expression will give us the speed of sound in the material."
    },
    {
        "instruction": "A 166 muF capacitor in series with a 28 ohm resistance is connected to a 238 V, 39 Hz supply. What is the time lag between the current maximum and voltage maximum?",
        "input": "Time_lag = atan(1 / (f * C * 10^-6 * 2 * pi * R)) / (2 * pi * f)",
        "output": "2.94e-03 s"
    },
    {
        "instruction": "Two point charges q1 = -180 x 10^(-6)C and q2 = 127 x 10^(-6)C are located 133 cm apart in vacuum. What is the electric field at the midpoint O of the line joining two charges?\n",
        "input": "Electric field = (q1 - q2) / (4 * pi * epsilon * r^2)",
        "output": "To calculate the electric field at the midpoint O, we use the formula:\nElectric field = (q1 - q2) / (4 * pi * epsilon * r^2)\nGiven q1 = -180 x 10^(-6)C, q2 = 127 x 10^(-6)C, and r = 133 cm,\nElectric field = 6.25e+06 newton/coulomb\n"
    },
    {
        "instruction": "A tank with a square base of area 14 m2 is divided by a vertical partition in the middle. The bottom of the partition has a small-hinged door of area 163 cm2. The tank is filled with water in one compartment, and an acid (of relative density 1.5) in the other, both to a height of 6 m. Compute the force necessary to keep the door closed.",
        "input": "6 * abs(1.5 - 1) * 0.98 * 163",
        "output": "The force necessary to keep the door closed is 479.2 Newton."
    },
    {
        "instruction": "Two bodies A, B of masses 49 kg and 193 kg respectively kept on a smooth, horizontal surface are tied to the ends of a tight string. A horizontal force F = 104 N is applied to B along the direction of the string. What is the acceleration and tension in the string?",
        "input": "",
        "output": "The acceleration is 0.4 m/s^2, and the tension is 21.1 N."
    },
    {
        "instruction": "Calculate the frequency of a sound wave whose wavelength is 554 m and speed is 199994 m/s in a given medium ?\n",
        "input": "Wavelength = Speed / Frequency",
        "output": "361 hz\nTo calculate the frequency of a sound wave, we can use the formula: Frequency = Speed / Wavelength. In this case, the speed of the sound wave is 199994 m/s and the wavelength is 554 m. Substituting these values into the formula, we can calculate the frequency: Frequency = 199994 m/s / 554 m"
    },
    {
        "instruction": "The coefficient of volume expansion of brass is 6.000000000000001e-05 K^-1. What is the change in its volume 80 m^3 for a rise in temperature from 95 degree C to 484 degree C?",
        "input": "Change in volume = d1 * a * (t2 - t1)",
        "output": "To find the change in volume, we use the following formula:\n\nChange in volume = d1 * a * (t2 - t1)\n\nSubstituting the given values into the formula, we find that the change in volume is approximately 1.87 m^3."
    },
    {
        "instruction": "An object is projected with an initial velocity of 603 m/s. If the maximum height reached by it is 6210 m, what is the angle of projection?",
        "input": "",
        "output": "35 degrees w.r.t. to the ground"
    },
    {
        "instruction": "Two sitar strings A and B playing the note \u2018Ga\u2019 are slightly out of tune and produce beats of frequency 22 Hz. The tension in the string A is slightly increased and the beat frequency is found to be 50 Hz. If the original frequency of A is 1249 Hz, what is the frequency of B?\n",
        "input": "Beat frequency = |f1+-f2|",
        "output": "1227 hertz\nFrequency decreases with a decrease in the tension of a string.\nThis is because frequency is directly proportional to the square root of tension."
    },
    {
        "instruction": "What is the gravitational field at a point P at a distance of 235 m from the center of the spherical shell of radius 279 m and mass 382 kg?",
        "input": "Gravitational Field (g) = 0 N/kg",
        "output": "The gravitational field at the specified point is zero."
    },
    {
        "instruction": "What is the gravitational field at the centre of the uniform solid sphere of radius 405 m and mass 112 kg?",
        "input": "Gravitational Field (g) = cal3(112, 405) N/kg",
        "output": "The gravitational field at the specified point is zero."
    },
    {
        "instruction": "Calculate root average velocity of a gas molecule having molar mass of 135 g/mol at 444 degree C. (R = 8.31 J/molK)",
        "input": "math.sqrt((8 * r * t1 * 1000) / (math.pi * m))",
        "output": "335.2457359014966 m/s\n The formula used is: math.sqrt((8 * r * t1 * 1000) / (math.pi * m))"
    },
    {
        "instruction": "In a circuit with a battery of potential difference 17 V, if the rate of heat generated is 461 W, calculate the current in the circuit?",
        "input": "I = P / V",
        "output": "27.1 ampere\n\nThe current in the circuit can be calculated using the formula: I = P / V, where P is the rate of heat generated and V is the potential difference."
    },
    {
        "instruction": "A convex lens produces a real image of height 57 cm at a distance of 61 cm from it of a real object having a height of 30 cm. At what distance is the object placed from the lens?",
        "input": "Formula: u = (v * ho) / hi",
        "output": "To find the distance at which the object is placed from the lens, we use the formula u = (v * ho) / hi, where u is the distance of the object from the lens, v is the distance of the image from the lens, hi is the height of the image, and ho is the height of the object. By substituting the given values into the formula, we can calculate u. In this case, the object is placed at a distance of 32.1 cm from the lens., this is the final The object is placed at a distance of 32.1 cm from the lens."
    },
    {
        "instruction": "Two long and parallel straight wires A and B carrying currents of 35 A and 30 A in the opposite direction are separated by a distance 62 cm. Estimate the force and its nature on the 33 cm section of wire A.",
        "input": "Force = (mu * i1 * i2 * l) / (2 * pi * r)",
        "output": "To calculate the force and its nature, we use the following formula:\n\nForce = (mu * i1 * i2 * l) / (2 * pi * r)\n\nSubstituting the given values:\n- mu = 4 * pi * 10^(-7) TmA^-1\n- i1 = 35 A\n- i2 = 30 A\n- r = 62 cm\n- l = 33 cm\n\nAfter evaluating the formula, we find that the force on the 33 cm section of wire is approximately 1.12e-04 newtons and repulsive."
    },
    {
        "instruction": "A 45 kg mass, fastened to the end of a steel wire of initial length 18 m, is whirled in a vertical circle with an angular velocity of 5 rev/s at the bottom of the circle. The cross-sectional area of the wire is 35 mm^2. Calculate the elongation of the wire when the mass is at the lowest point of its path.",
        "input": "elongation = (force * length) / (A * 10^(-6) * Y_steel)",
        "output": "To calculate the elongation, we use the formula:\n\nelongation = (force * length) / (A * 10^(-6) * Y_steel)\n = (45 kg * (9.8 + 18 m * \u03c0^2 * 5^2) * 18 m) / (35 mm^2 * 10^(-6) m^2 * (2 * 10^11 N/m^2))\n = 51.5 cm."
    },
    {
        "instruction": "What is the electric field at a point P at a distance of 491 m from the center of the spherical shell of radius 497 m and having -1.56e-06 C charge distributed uniformly on it?",
        "input": "Electric Field (E) = 0 N/C",
        "output": "0 newton/coulomb\nFor a spherical shell, the electric field inside the shell is zero."
    },
    {
        "instruction": "If a gas molecule has root mean square velocity of 1657 m/s and is at a temperature 2 degree C. What is the molar mass of the gas. (R = 8.31 J/molK)",
        "input": "(3 * r * t1 * 1000) / (v * v)",
        "output": "12.847945968330256 m/s\n The formula used is: (3 * r * t1 * 1000) / (v * v)"
    },
    {
        "instruction": "A 57 cm long metallic rod is rotated with an angular frequency of 64 rad s-1 about an axis normal to the rod passing through one of its ends. The other end of the rod is in contact with a circular metallic ring. A uniform magnetic field of 55 T parallel to the axis exists everywhere. Find the EMF developed between the center and the ring.\n",
        "input": "EMF = (B * l * w^2) / 2",
        "output": "6.42e+06 volt\n\n\nThe electromotive force (EMF) can be calculated using the formula EMF = (B * l * w^2) / 2, where B is the magnetic field magnitude, l is the length of the metallic rod, and w is the angular frequency of rotation in radians per second."
    },
    {
        "instruction": "What is the gravitational potential at the center of the uniform solid sphere of radius 92 m and mass 291 kg?",
        "input": "Gravitational Potential (V) = cal3(291, 92) joule/kg",
        "output": "The gravitational potential at the center of the uniform solid sphere of radius 92 m and mass 291 kg is given by the formula V = (-3 * G * m) / (2 * r), where G is the gravitational constant, m is the mass, and r is the distance. Plugging in the values, we get V = -3.16e-10 joule/kg."
    },
    {
        "instruction": "In a process, 1460 J of heat is absorbed by a system and 4041 J of work is done by the system. What is the change in internal energy for the process ?\n",
        "input": "\u0394U = Q+W",
        "output": "from first law of thermodynamics, du = q + w => du = (+1460) + (-4041) => du = -2581joule\nQ is positive and W is negative as heat is absorbed by a system and work is done by system."
    },
    {
        "instruction": "A bullet fired at an angle of 71 degrees with the horizontal hits the ground 342 m away. By adjusting its angle of projection, can one hope to hit a target 224 m away?",
        "input": "yes",
        "output": "The target can be hit."
    },
    {
        "instruction": "For a CE-transistor amplifier, the audio signal voltage across the collected resistance of 3660 ohm is 19 V. Suppose the current amplification factor of the transistor is 180, find the input signal voltage if the base resistance is 1930 ohm?\n",
        "input": "output voltage/input voltage = current amplification factor*output resistance/input resistance",
        "output": "voltage without amplification is 19/180 = 0.11, to get voltage per unit resistance, we need to divide it by 3660, to get to original voltage, we need to multiply per unit resistance voltage with base resistance 1930 doing all that we get, 5.57e-02 volt\n"
    },
    {
        "instruction": "A meter stick of mass 47 g is balanced on a knife edge at its center. Where will the stick be balanced when a coin of mass 88 g is put at the 16 mark?",
        "input": "Balance Position = ((50 * m) + (m1 * t1)) / (m + m1)",
        "output": "The stick will be balanced at approximately 27.8 cm.\nBalance Position = ((50 * 47) + (88 * 16)) / (47 + 88)"
    },
    {
        "instruction": "A circular coil of wire consisting of 80 turns, each of radius 711 cm placed in a horizontal plane carries a current of 3 A in anticlockwise direction. What is the magnitude and direction of the magnetic field B at the center of the coil?",
        "input": "B = (mu * n * i) / (2 * r)",
        "output": "To calculate the magnetic field B at the center of the coil, we use the following formula:\n\nB = (mu * n * i) / (2 * r)\n\nWhere,\n- B = Magnetic field at the center of the coil\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- n = Number of turns in the coil\n- i = Current flowing through the coil\n- r = Radius of the coil\n\nSubstituting the given values into the formula, we find that the magnitude of the magnetic field B is approximately 2.12e-05 tesla vertically upwards."
    },
    {
        "instruction": "What is the pressure inside a drop of liquid of radius 3 mm at room temperature? Surface tension of liquid at that temperature (347 K) is 1020 x 10^(-3) Nm^(-1). Also give the excess pressure inside the drop.",
        "input": "excess pressure = (2 * surface tension) / radius, total pressure = 1.01 * (10 ** 5) + excess pressure",
        "output": "The excess pressure inside the drop is 680.00 pascal. The total pressure inside the drop is 1.02e+05 pascal."
    },
    {
        "instruction": "A long straight wire in the horizontal plane carries a current of of 117 A in north to south direction. What is the magnitude and direction of the magnetic field B at a point 1069 cm west of the wire.\n",
        "input": "B = (mu * i) / (2 * pi * r)",
        "output": "To calculate the magnitude and direction of the magnetic field B, we use the following formula:\n\nB = (mu * i) / (2 * pi * r)\n\nWhere,\n- B = Magnetic field\n- mu = Permeability of free space (4 * pi * 10^(-7) T*m/A)\n- i = Current flowing through the wire\n- r = Distance from the wire\n\nSubstituting the given values into the formula, we find that the magnitude and direction of the magnetic field B is approximately 2.2e-06 tesla vertically downwards\n."
    },
    {
        "instruction": "Two bodies A, B of masses 130 kg and 45 kg respectively kept on a smooth, horizontal surface are tied to the ends of a tight string. A horizontal force F = 50 N is applied to A along the direction of the string. What is the acceleration and tension in the string?",
        "input": "",
        "output": "The acceleration is 0.3 m/s^2, and the tension is 12.9 N."
    },
    {
        "instruction": "A capacitor with air between it's parallel plates, each plate has an area of 0.0179 m2 and the distance between the plates is 490 mm. Calculate the capacitance of the capacitor?\n",
        "input": "C = (\u03b5\u2080 * A) / d",
        "output": "3.23e-01 pico-farad\n\n\n Explanation: To calculate the capacitance C of a capacitor with air between its parallel plates, we use the formula above. In the formula, \u03b5\u2080 represents the permittivity of free space, A represents the area of each plate, and d represents the distance between the plates. By multiplying the permittivity of free space by the plate area and dividing it by the plate separation, we can determine the capacitance of the capacitor"
    },
    {
        "instruction": "Given observations (tuples of I (in A) and V (in V)): (6, 108), (7, 126), (11, 198), (16, 286), (22, 396), (28, 504); Determine whether the given conductor is an ohmic conductor or not.\n",
        "input": "",
        "output": "No, it is not an ohmic conductor.\n"
    },
    {
        "instruction": "What is the side of a cube of volume 723.115 cm3 (in m).\n",
        "input": "Volume = side^3",
        "output": "8975716\nCube of the side is it's volume."
    },
    {
        "instruction": "A 9936 N force is applied on a body placed on a smooth surface resulting in acceleration of 466 m/s^2, then what is the mass of the body?",
        "input": "m = F / a",
        "output": "21.321888412017167\nTo calculate the mass, we use the formula m = F / a, where m is the mass, F is the force (9936 N), and a is the acceleration (466 m/s^2)."
    },
    {
        "instruction": "An object of mass 3226 g stands on a weighing machine in a lift, which is moving upwards with a uniform acceleration of 369 cm/s^2.",
        "input": "Scale Reading = m * (10 + (acc / 100))",
        "output": "44.2\nTo calculate the scale reading, we use the formula Scale Reading = mass * (10 + (acceleration / 100)), where the mass is 3226 g and the acceleration is 369 cm/s^2."
    },
    {
        "instruction": "A rod of mass 2235 kg has a length of 45 m. What is the moment of inertia with respect to its end?",
        "input": "Moment of Inertia = (Constant) * mass * length^2",
        "output": "The moment of inertia with respect to its end is approximately 1508625.0 kgm^2.\n\nMoment of Inertia = (Constant) * mass * length^2\n\nConstant = 0.3333333333333333\nmass = 2235 kg\nlength = 45 m"
    },
    {
        "instruction": "A concave lens produces 56 times diminished real image of height 34.53 cm of an object placed in front of it. What is the height of the object?",
        "input": "Formula: ho = n * hi",
        "output": "To find the height of the object, we use the formula ho = n * hi, where ho is the height of the object, hi is the height of the image, and n is the magnification factor. By substituting the given values into the formula, we can solve for ho. In this case, the height of the object is 1933.7 cm., this is the final The height of the object is 1933.7 cm."
    },
    {
        "instruction": "If a physical quantity P=(a^1.5)*(b^-1.0)*(c^-2.0), the percentage errors of measurement in a,b,c are 2%,3%,1% respectively. If the calculated value of P is 17 then what is maximum error possible.\n",
        "input": "Percentage Error in P = |dP/P| * 100",
        "output": "1.36\nTo find the maximum possible error in the calculated value of P, we can use the concept of percentage error propagation. The formula to calculate the percentage error in a quantity calculated from measured quantities is given by: Percentage Error in P = |dP/P| * 100, where dP is the maximum absolute error in P. Since P = (a^1.5)*(b^-1.0)*(c^-2.0), we can differentiate the expression with respect to each measured quantity (a, b, c) to find the maximum absolute error for each term. Then we can substitute the given percentage errors and calculated value of P to find the maximum error. Let's calculate the maximum error using the given information."
    },
    {
        "instruction": "A 190 mH inductor is connected to 23 V, 156 Hz ac supply. Determine the rms value of current in the circuit?",
        "input": "X_l = 2 * pi * f * L * 0.001\nI_rms = V / X_l",
        "output": "1.24e-01 ampere"
    },
    {
        "instruction": "If a car has an initial velocity of 189 m/s and has a constant acceleration of 2 m/s\u00b2, then what is the time taken by the car to attain a velocity of 350 m/s?",
        "input": "time = (final_velocity - initial_velocity) / acceleration",
        "output": "The time taken by the car to attain a velocity of 350 m/s is 80.5 s."
    },
    {
        "instruction": "An aircraft of mass 113 kg executes a horizontal loop at a speed of 294 m/s with its wings banked at 11 degrees. What is the radius of the loop?",
        "input": "(v^2) / (g * tan((param * pi) / 180))",
        "output": "44467\nTo calculate the radius, we use the formula (v^2) / (g * tan((param * pi) / 180)), where v is the speed (294 m/s), g is the acceleration due to gravity (10 m/s^2), and param is the angle of banking (11 degrees)."
    },
    {
        "instruction": "A concave lens produces 68 times diminished real image at a distance of 9.74 cm from the lens. At what distance is the object placed in front of the lens?",
        "input": "Formula: u = n * v",
        "output": "To find the distance at which the object is placed, we use the formula u = n * v, where u is the distance of the object from the lens, v is the distance of the image from the lens, and n is the magnification factor. By substituting the given values into the formula, we can solve for u. In this case, the object is placed at a distance of 662.3 cm., this is the final The object is placed at a distance of 662.3 cm."
    },
    {
        "instruction": "A 9121 N force is applied on a body placed on a smooth surface resulting in acceleration of 426 m/s^2, then what is the mass of the body?",
        "input": "m = F / a",
        "output": "21.4\nTo calculate the mass, we use the formula m = F / a, where m is the mass, F is the force (9121 N), and a is the acceleration (426 m/s^2)."
    },
    {
        "instruction": "A concave lens produces a real image at a distance of 56 cm from it of a real object having a height of 54 cm and placed 78 cm in front of it. What is the height of the image?",
        "input": "Formula: hi = (v * ho) / u",
        "output": "To find the height of the image, we use the formula hi = (v * ho) / u, where hi is the height of the image, ho is the height of the object, u is the distance of the object from the lens, and v is the distance of the image from the lens. By substituting the given values into the formula, we can solve for hi. In this case, the height of the image is 38.8 cm., this is the final The height of the image is 38.8 cm."
    },
    {
        "instruction": "Estimate the distance for which ray optics is good approximation for an aperture of 16 mm and wavelength 343 nm.\n",
        "input": "Fresnel Distance = Aperture^2/Wavelength of light",
        "output": "7.46e+08 m\nThe criterion for ray optics to be a good approximation is when the size of the aperture is much larger than the wavelength of light. This condition ensures that the wave nature of light can be neglected, and light can be treated as a ray.To estimate the distance for which ray optics is a good approximation, we can use the following formula: Distance \u2248 2 * (aperture size)^2 / (wavelength)"
    },
    {
        "instruction": "A stone is thrown vertically upward with an initial velocity of 6443.53 m/s under gravity. What is the maximum height attained by the stone?",
        "input": "initial velocity (u) = 6443.53 m/s",
        "output": "maximum height (h) = (initial velocity (u)\u00b2) / (2 * acceleration (g))\nh = (6443.53\u00b2) / (2 * 9.8)\nh = 41519078.8609 / 19.6\nh = 2118320.4"
    }
]