Two particles $X$ and $Y$,initially at rest,move towards each other under mutual attraction. If at any instant the velocity of particle $X$ is $V$ and the velocity of particle $Y$ is $2V$,then the velocity of their center of mass will be:

$A$ body of mass $2 \,kg$ is moving towards north with a velocity of $20 \,m \,s^{-1}$ and another body of mass $3 \,kg$ is moving towards east with a velocity of $10 \,m \,s^{-1}$. The magnitude of the velocity of the centre of mass of the system of the two bodies is

Two masses of $1 \ kg$ and $2 \ kg$ are hanged from a pulley as shown in the figure. If the system starts from rest,find the distance travelled by the centre of mass in the first two seconds.

If one observes from the reference frame in which the centre of mass appears to be at rest,what will be the velocity of the centre of mass?

Explain translational motion by the given illustration.

$A$ small ball $B$ of mass $m$ is suspended with a light inelastic string of length $L$ from a block $A$ of the same mass $m$,which can move on a smooth horizontal surface as shown in the figure. The ball is displaced by an angle $\theta$ from the equilibrium position and then released. The displacement of the block when the ball reaches the equilibrium position is