Two particles $A$ and $B$ initially at rest move towards each other under a mutual force of attraction. At the instant when the velocity of $A$ is $v$ and that of $B$ is $2v$,the velocity of the centre of mass of the system is:

Two particles of masses $1 \,g$ and $2 \,g$ move towards each other with velocities $10 \,ms^{-1}$ and $20 \,ms^{-1}$ respectively. The velocity of the centre of mass of the system of the two particles is (in $\,ms^{-1}$)

$A$ system consists of two particles of masses $m_1$ and $m_2$. If the particle of mass $m_1$ is moved towards the centre of mass through a distance $d$,then the distance the second particle should be moved,so as to keep the centre of mass at the same position is

Two bodies of masses $m_1$ and $m_2$ are connected by a massless string passing over a massless,frictionless pulley as shown in the figure. Given $m_2 < m_1$. The acceleration of the center of mass of the system is:

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

$A$ $500 \ kg$ boat is $9 \ m$ long and is floating without motion on still water. $A$ man of mass $100 \ kg$ is at one end. If he runs to the other end of the boat and stops,the displacement of the boat is: