$A$ ball is thrown with a velocity of $6\, m/s$ vertically downwards from a height $H = 3.2\, m$ above a horizontal floor. If it rebounds back to the same height,then the coefficient of restitution $e$ is $[g = 10\, m/s^2]$.

$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ particle of mass $m$ strikes the rod at one end with a velocity $v$ perpendicular to the rod. If the particle comes to rest after the collision,the velocity of the center of mass of the rod after the collision is:

$A$ $1 \,kg$ ball moving at $12 \,ms^{-1}$ collides with a $2 \,kg$ ball moving in the opposite direction at $24 \,ms^{-1}$. If the coefficient of restitution is $2/3$, then their velocities after the collision are

$A$ ball falls freely from rest from a height of $6.25 \ m$ onto a hard horizontal surface. If the ball reaches a height of $81 \ cm$ after the second bounce from the surface,the coefficient of restitution is

Ball $1$ collides with another identical ball at rest. For what value of coefficient of restitution $e,$ the velocity of the second ball becomes two times that of the first ball after the collision?

$A$ 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?