$A$ man inside a freely falling box throws a heavy ball towards a side wall. The ball keeps on bouncing between the opposite walls of the box. We neglect air resistance and friction. Which of the following figures depicts the motion of the centre of mass of the entire system (man,the ball and the box)?

Two blocks of masses $2 \,kg$ and $1 \,kg$ are tied to the ends of a string which passes over a light frictionless pulley. The blocks are held at rest at the same horizontal level and then released suddenly. The distance traversed by their centre of mass in $2 \,s$ is (acceleration due to gravity $g = 10 \,ms^{-2}$) (in $\,m$)

Discuss the explosion of a projectile.

Are you in agreement with the statement: "The velocity of all particles of a system is equal to the velocity of the centre of mass"?

Two identical particles are moving with velocities $2v$ and $v$ respectively. Find the velocity of the center of mass.

Two blocks of masses $m$ and $2m$ are connected by a massless string which passes over a fixed frictionless pulley. If the system of blocks is released from rest,the speed of the centre of mass of the system of two blocks after a time of $5.4 \ s$ is (Acceleration due to gravity $= 10 \ ms^{-2}$) (in $ms^{-1}$)