$A$ ball $P$ of mass $0.5 \ kg$ moving with a velocity of $10 \ ms^{-1}$ collides with another ball $Q$ of mass $1 \ kg$ at rest. If the coefficient of restitution is $0.4$,the ratio of the velocities of the balls $P$ and $Q$ after the collision is

$A$ sphere strikes a wall and rebounds with a coefficient of restitution $e = 1/3$. If it rebounds with a velocity of $0.1 \ m/s$ at an angle of $60^{\circ}$ to the normal to the wall,the percentage loss of kinetic energy is:

$A$ small steel ball bounces on a steel plate held horizontally. On each bounce, the speed of the ball arriving at the plate is reduced by a factor $e$ (coefficient of restitution) in the rebound, so that $V_{\text{upward}} = e V_{\text{downward}}$. If the ball is initially dropped from a height of $0.4 \text{ m}$ above the plate and if $10 \text{ s}$ later the bouncing ceases, the value of $e$ is:

$A$ ball moving with velocity $2 \, m/s$ collides head-on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$,then their velocities after collision will be

Two balls of equal mass undergo head-on collision while each was moving with speed $6 \, m/s$ in opposite directions. If the coefficient of restitution is $e = 1/3$,the speed of each ball after impact will be ............ $m/s$.

$A$ ball of mass $m$ is moving with a speed $V$ as shown in the figure. It undergoes an inelastic collision with a ball of mass $2m$ which was initially at rest. The velocity of the ball of mass $2m$ after the collision is given by