What happens if I hold a piece of paper horizontally with two hands and I let go of one hand?
If you hold a piece of paper horizontally with two hands and let go of one hand, the paper will tilt downwards on the side of the hand you released. This happens because the center of gravity of the paper and your hands is shifted towards the side that still has your hand holding it, causing the unbalanced force to pull the paper downwards. If you don't intervene and still hold the paper on one hand, the paper will find a new balance hanging from your other hand.
I don't fully agree. Center of gravity of paper is still at the center of the sheet. But it will truly tilt downward. But not because center of gravity shifted, but because the second support was removed. What do you think about it?