A body of mass ' $m$ ' moving with a velocity of ' $v$ ' collides head on with another body of mass ' 2 m ' at rest. If the coefficient of restitution between the two bodies is ' $~ e$ ', then the ratio of the velocities of the two bodies after collision is

A solid cylinder of mass 2 kg , length 40 cm and radius 10 cm is placed in contact with a solid sphere of mass 0.5 kg and radius 10 cm such that the centres of the two bodies lie along the geometrical axis of the cylinder. The distance of the centre of mass of the system of two bodies from the centre of the sphere is

Two blocks of masses in the ratio $m: n$ are connected by a light inextensible string passing over a frictionless fixed pulley. If the system of the blocks is released from rest, then the acceleration of the centre of mass of the system of the blocks is

( $g=$ acceleration due to gravity)

A ball $A$ of mass 1.2 kg moving with a velocity of $8.4 \mathrm{~ms}^{-1}$ makes one-dimensional elastic collision with a ball $B$ of mass 3.6 kg at rest. The percentage of kinetic energy transferred by ball $A$ to ball $B$ is