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Q. A child is standing at one end of a long trolley moving with a speed $v$ on a smooth horizontal floor. If the child starts running towards the other end of the trolley with a speed $u$, the centre of mass of the system (trolley + child) will move with a speed

System of Particles and Rotational Motion

Solution:

The speed of the centre of mass of the system remains unchanged (equal to $v$) because no external force acts on the system. The forces involved in running on the trolley are internal to this system.