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 ?

A child sits stationary at one end of a long trolley moving uniformly

1.	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» Solution :The running of the child will produce no effect on the velocity of centre of MASS of the trolley. Because trolley and child has same system and FORCE and due to it child motion is PURELY internal. Since no EXTERNAL force is involved in the child-trolley system, the child.s motion will produce no change in the velocity of the centre of mass of the trolley. As a result system of child and trolley have centre of mass with CONSTANT speed.