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Q. A man inside a freely falling box throws a heavy ball towards a side wall. The ball keeps on bouncing between the opposite walls of the box. We neglect air resistance and friction. Which of the following figures depict the motion of the centre of mass of the entire system (man, the ball and the box)?

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Solution:

The centre of mass will move downward as the whole system is falling. There is no external force on the system of the man, the ball and the box in the horizontal direction, so the system will not move in the horizontal direction. In the horizontal direction, when the ball collides with the walls, the ball and the box wall moves such that their centre of mass is at rest in horizontal direction.