A child is standing at one end of a long trolley moving with a speed v on a smooth horizontal track. 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
The speed of the centre of mass of a system can change only if a net external force acts on it. The forces involved (such as the action and reaction and frictional forces), when the child runs on the trolley, are internal to the (trolley + child) system. The speed of the centre of mass of the system will remain unchanged, i.e., equal to v. Hence, the correct choice is (d).