Two particles $A$ and $B$ (both initially at rest) start moving towards each other under a mutual force of attraction. At the instant,when the speed of $A$ is $v$ and the speed of $B$ is $2v$,the speed of the centre of mass is

$A$ 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:

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 $\,ms^{-1}$)

The centre of mass of two masses $m$ and $m'$ moves by a distance $\frac{x}{5}$ when mass $m$ is moved by a distance $x$ and $m'$ is kept fixed. The ratio $\frac{m'}{m}$ is

$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ horizontal force $F$ is applied at one end of the rod perpendicular to its length. The acceleration of the centre of mass of the rod is:

Two blocks of masses $10\,kg$ and $4\,kg$ are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of $14\,m/s$ to the heavier block in the direction of the lighter block. The velocity of the centre of mass is ........ $m/s$.