Two bodies of masses $2 \ kg$ and $4 \ kg$ are moving with velocities $20 \ m/s$ and $10 \ m/s$ towards each other due to mutual gravitational attraction. What is the velocity of their centre of mass (in $m/s$)?

$A$ ball of mass $M$ moving with a speed of $2 \ m \ s^{-1}$ hits another ball of mass $1 \ kg$ moving in the same direction with a speed of $1 \ m \ s^{-1}$. If the kinetic energy of the center of mass is $4/3 \ J$,then the magnitude of $M$ is: (in $kg$)

Two particles of mass $m_1$ and $m_2$ are separated by a distance $d$. If the first particle is moved towards the centre of mass by a distance $x$,then the distance by which the second particle must be moved towards the centre of mass to keep the centre of mass at the same position is:

Two particles have masses $m_1$ and $m_2$. If the first particle $(m_1)$ is moved by a distance $d$ towards the center of mass,by what distance should the second particle $(m_2)$ be moved so that the center of mass of the system remains at the same position?

$A$ ball of mass $m$ is thrown upward and another ball of same mass is thrown downward so as to move freely under gravity. The acceleration of the centre of mass is .........

$A$ body of mass $20 \ kg$ is moving with a velocity of $2v$ and another body of mass $10 \ kg$ is moving with velocity $v$ along the same direction. The velocity of their centre of mass is