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

Two particles of masses $3 \ kg$ and $6 \ kg$ are approaching towards each other with accelerations $2 \ m/s^2$ and $4 \ m/s^2$ respectively,on a smooth horizontal surface. Then the acceleration of the centre of mass of the system is ..... $m/s^2$.

$A$ system consists of two particles of masses $m_1$ and $m_2$ separated by a distance $r$. If the particles move towards each other with velocities $v_1$ and $v_2$ respectively,the velocity of the centre of mass of the system is:

The figure shows a man of mass $m$ standing at the end $A$ of a trolley of mass $M$ placed at rest on a smooth horizontal surface. The man starts moving towards the end $B$ with a velocity $u_{rel}$ with respect to the trolley. The length of the trolley is $L$. The distance moved by the man with respect to ground is

Two balls are thrown in the air. The second ball is thrown $2 \ s$ after the first ball. What is the acceleration of the center of mass of the two balls while they are in the air?

Two bodies of masses $2\,kg$ and $4\,kg$ are moving with velocities $2\,m/s$ and $10\,m/s$ respectively towards each other due to mutual gravitational attraction. What is the velocity of their centre of mass,given that the bodies were at rest initially?