Question

A child sits stationary at one end of a long trolley moving uniformly with a speed V on a smooth horizontal floor. If the child gets up and runs about on the trolley in any manner, what is the speed of the CM of the (trolley + child) system ?

Answer 1

It is necessary that an external force is applied on a system to change its motion.

In this case, the boy is running arbitrarily on trolley with velocity v, which produces only internal forces in the system. The internal force cannot affect the motion of the system. As there is no external force on the system, so the speed of the centre of mass of the trolley and child system will remain same.