A body of mass 2 kg is moving towards north with a velocity of $20 \mathrm{~ms}^{-1}$ and another body of mass 3 kg is moving towards east with a velocity of $10 \mathrm{~ms}^{-1}$. The magnitude of the velocity of the centre of mass of the system of the two bodies is

A body falls freely on to a hard horizontal surface. If the coefficient of restitution between the surface and the body is 0.8 , then the ratio of the maximum height to which the body rises after second impact and the initial height of the body is

Two bodies of masses $M$ and $4 M$ initially at rest, start moving towards each other due to their mutual attraction. The velocity of their centre of mass when the first body attains a velocity $v_0$ is

A body of mass ' $m$ ' moving along a straight line collides with a stationary body of mass ' $2 m^{\prime}$. After collision if the two bodies move together with the same velocity, then the fraction of kinetic energy lost in the process is