Question

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 will move with a speed ?

Answer 1

v

Explanation:

no external force acts on the body. Therefore, velocity of center of mass remains the same.

mv/m=m

Answer 2

The velocity of the centre of mass will remain unchanged and It will be v

• When the child stands on a trolley, both the child and trolley move with the same velocity that is v.
• Thus, the centre of mass is also moving with the velocity of vehicle. Thus, the equation will be - vcom = mv + Mv / (m + M) = v
• The center of mass velocity only changes when the system is subjected to net external force.  
• But since when the child runs on the trolley the only forces involved in the child + trolley system are internal.