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test.json
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[
{
"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."