$A$ ball impinges directly on a similar ball of same mass at rest. If $1/4$ of the kinetic energy is lost by the impact,the value of the coefficient of restitution is

$A$ particle of mass $m$ strikes the ground inelastically with a coefficient of restitution $e$. Find the relation between the angles $\theta$ and $\alpha$ as shown in the figure.

$A$ ball of mass $M$ falls from a height $h$ on a floor. If the coefficient of restitution is $e$,the height attained by the ball after two rebounds is

$A$ bullet of mass $m$ and speed $v$ hits a pendulum bob of mass $M$ at time $t_1$,and passes completely through the bob. The bullet emerges at time $t_2$ with a speed of $v/2$. The pendulum bob is suspended by a stiff rod of length $l$ and negligible mass. After the collision,the bob can barely swing through a complete vertical circle. At time $t_3$,the bob reaches the highest position. What quantities are conserved in this process?

$A$ $2 \,kg$ ball moving at $24 \,ms^{-1}$ undergoes inelastic head-on collision with a $4 \,kg$ ball moving in the opposite direction at $48 \,ms^{-1}$. If the coefficient of restitution is $2/3$, their velocities in $ms^{-1}$ after impact are

In an inelastic collision,after collision the kinetic energy