$A$ 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 $m/s$?

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

$A$ steel sphere of radius $1.2 \ cm$ collides with a second steel sphere at rest. If the collision is elastic and after the collision the first sphere continues to move in its initial direction with a velocity of $\frac{7}{9}$ times its initial velocity,then the radius of the second sphere is (in $cm$)

On a horizontal smooth surface,a disc of radius $r$ is placed at rest. Another disc of the same mass is moving towards it with an impact parameter equal to its own radius. What should be the radius of the incoming disc so that after the collision,the first disc moves at an angle of $45^{\circ}$ to the direction of motion of the incoming disc?

$A$ body of mass $m$ moving with velocity $v$ makes a head-on collision with another body of mass $2m$ which is initially at rest. What is the ratio of the kinetic energy of the colliding body before and after the collision (in $: 1$)?

$A$ particle of mass $m$ moving with velocity $v$ makes a perfectly elastic collision with a simple pendulum bob of mass $m$. After the collision,the maximum height attained by the bob is: