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

A disc of mass 0.2 kg is kept floating in air without falling by vertically firing bullets each of mass 0.05 kg on the disc at the rate of 10 bullets per every second. If the bullets rebound with the same speed, then the speed of each bullet is

(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A body moving along a straight line collides another body of same mass moving in the same direction with half of the velocity of the first body. If the coefficient of restitution between the two bodies is 0.5 , then the ratio of the velocities of the two bodies after collision is (Treat the collision as one dimensional)