Two particles which are initially at rest,move towards each other under the action of their internal attraction. If their speeds are $v$ and $2v$ at any instant,then the speed of centre of mass of the system 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

The velocity of the centre of mass of the system as shown in the figure is

Two particles of masses $m_1$ and $m_2$ $(m_1 > m_2)$,initially at rest,move towards each other under an inverse square law force of attraction. Pick out the correct statement about the centre of mass $(CM)$ of the system.

In the system of two particles of masses $m_1$ and $m_2$,the first particle is moved by a distance $d$ towards the centre of mass. To keep the centre of mass unchanged,the second particle will have to be moved by a distance

$A$ trolley of length $L$ has a pistol fixed on its wall as shown in the figure. The mass of the (trolley + pistol) is $M$. $A$ bullet of mass $m$ is fired from the pistol with a velocity $v_0$ and hits the opposite wall. What is the distance moved by the trolley during the time the bullet travels to hit the opposite wall?