$A$ ball is dropped from a height $h_0$. It undergoes $n$ collisions with the ground. If the velocity of the ball after $n$ rebounds is $u_n$ and it reaches a height $h_n$,which formula gives the coefficient of restitution $e$?

$A$ ball strikes a smooth horizontal ground at an angle of $45^o$ with the vertical. What cannot be the possible angle of its velocity with the vertical after the collision? (Assume $e \leq 1$ ).

$A$ 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 $v$?

$A$ ball is dropped from a height $h$ onto a ground level. If the coefficient of restitution is $e$,what is the height reached by the ball after the $n^{th}$ bounce?

$A$ particle of mass $m$ moving with speed $2v$ collides with a mass $2m$ moving with speed $v$ in the same direction. After the collision,the first mass is stopped completely,while the second one splits into two particles each of mass $m$,which move at an angle of $45^o$ with respect to the original direction. The speed of each of the moving particles will be:

Two identical balls $A$ and $B$ of equal mass $m$ are lying on a smooth surface as shown in the figure. If ball $A$ hits ball $B$ at rest with a velocity $16 \,ms^{-1}$,then the coefficient of restitution $e$ between $A$ and $B$ so that $B$ just reaches the highest point of the smooth inclined plane of height $5 \,m$ is $\left(g=10 \,ms^{-2}\right)$