For a perfectly elastic collision,the coefficient of restitution $e$ is

$A$ ball is dropped from a height of $10 \ m$ and hits the roof of an elevator moving downwards with a velocity of $1 \ m/s$. What is the rebound velocity of the ball in $m/s$?

$A$ body of mass $2 \ kg$ makes an elastic collision with another body at rest and continues to move in the original direction with one-fourth of its original speed. The mass of the second body which collides with the first body is ............... $kg$.

$A$ sphere of mass $0.1 \ kg$ is attached to a string of length $1 \ m$. It is released from a horizontal position and collides with another sphere of equal mass $m$ at rest. Find the kinetic energy gained by the second sphere. The collision is perfectly elastic. (in $J$)

Two billiard balls of mass $0.05\,kg$ each,moving in opposite directions with $10\,m/s$,collide and rebound with the same speed. If the time duration of contact is $t = 0.005\,s$,then the force exerted on the balls due to each other is $\dots N$.

$A$ sphere of mass $m$,moving with velocity $3u$,collides head-on with another identical sphere at rest. If $e$ is the coefficient of restitution,what will be the ratio of the velocity of the second sphere to that of the first sphere after the collision?