$A$ ball with a coefficient of restitution $e = 0.5$ is dropped from a certain height. What is the percentage loss in kinetic energy after each bounce?

$A$ ball is dropped from a height of $5 \ m$ on a planet. It rebounds to a height of $1.8 \ m$. What is the fraction of velocity lost by the ball?

Two pendulums with identical bobs and lengths are suspended from a common support such that in rest position the two bobs are in contact (figure). One of the bobs is released after being displaced by $10^{\circ}$ so that it collides elastically head-on with the other bob.
$(a)$ Describe the motion of two bobs.
$(b)$ Draw a graph showing variation in energy of either pendulum with time,for $0 \leqslant t \leqslant 2T$,where $T$ is the period of each pendulum.

$A$ ball is dropped from a height of $20\,m$. If the coefficient of restitution for the collision between ball and floor is $0.5$,after hitting the floor,the ball rebounds to a height of $.............m$.

$A$ glass ball collides with a smooth horizontal surface with a velocity $\vec{v} = a \hat{i} - b \hat{j}$. If the coefficient of restitution of the collision is $e$,find the velocity of the ball just after the collision. ($x$-axis is along the ground and $y$-axis is along the vertical).

Ball $P$ of mass $m$ moving with velocity $v$ collides with another ball $Q$ of mass $2m$,which is at rest. If $v_P$ and $v_Q$ are the final velocities of $P$ and $Q$ respectively after the collision,then (Assume the coefficient of restitution is $e = 1/3$):