$A$ 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

In free space,a shell moving with velocity $60\,m/s$ along the positive $x$-axis passes through the origin and explodes into two pieces with a mass ratio of $1:2$. After the explosion,the velocity of the centre of mass is ....... $m/s$.

Two men of masses $55 \ kg$ and $65 \ kg$ are standing at the opposite ends of a boat. The length of the boat is $3.0 \ m$ and its mass is $100 \ kg$. The $55 \ kg$ man walks up to the $65 \ kg$ man and sits beside him. If the boat is in still water,the center of mass of the system will shift by ..... $m$.

Three men $A, B$ and $C$ of masses $40\,kg, 50\,kg$ and $60\,kg$ are standing on a plank of mass $90\,kg$,which is kept on a smooth horizontal plane. If $A$ and $C$ exchange their positions,then mass $B$ will shift:

$M$ mass of a man stands at one end of a plank of length $L$ which lies at rest on a frictionless surface. The man walks to the other end of the plank. If the mass of the plank is $\frac{M}{3}$,then the distance that the man moves relative to the ground is:

Two particles $A$ and $B$,initially at rest,move towards each other under a mutual force of attraction. At an instance when the speed of $A$ is $v$ and the speed of $B$ is $2v$,the speed of the centre of mass $(CM)$ is: