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When the child is standing on the trolley, both child and trolley are moving with the same velocity = v
So, their centre of mass is also moving with the velocity of the vehicle,
vcom = mv + Mv / (m + M) = v
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the velocity of centre of mass changes only if the system is subjected to net external force. But since the only forces involved in the child + trolley system are internal(action-reaction pair) when the child runs on the trolley. Therefore, the velocity of their centre of mass will remain unchanged. It will be v
Thus the answer is option 3.
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