$A$ ball kept at $20 \,m$ height falls freely in a vertically downward direction and hits the ground. The coefficient of restitution is $0.4$. What is the velocity of the ball after the first rebound (in $\,ms^{-1}$)? $\left[g=10 \,ms^{-2}\right]$

$A$ ball is dropped from a height $h$. It bounces repeatedly. Find the height attained by the ball after $n$ bounces and the time taken by the ball to complete $n$ bounces.

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 $P$ 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

$A$ particle of mass $m_1$ moving along the $X$-axis collides with a stationary particle of mass $m_2$ and deviates by an angle $30^{\circ}$ to the $X$-axis as shown in the figure. If the percentage change in kinetic energy of the combined system of these two particles reduces by $50 \%$,then the ratio of the masses $\frac{m_2}{m_1}$ is

$A$ large ball of mass $M$,moving with velocity $u$,strikes a small ball of mass $m$,which is at rest. After the collision,the small ball attains velocity $u$ and the large ball attains velocity $v$. What is the value of $v$?