$A$ sphere of mass $M$ moving with velocity $u$ undergoes a perfectly elastic collision with a stationary sphere of mass $m$. If their velocities after the collision are $V$ and $v$ respectively,what is the value of $v$?

$A$ billiard ball of mass $M$,moving with velocity $v_1$ collides with another ball of the same mass but at rest. If the collision is elastic,the angle of divergence after the collision is (in $^{\circ}$)

$A$ body of mass $M$ moving at speed $V_{0}$ collides elastically with a mass $m$ at rest. After the collision,the two masses move at angles $\theta_{1}$ and $\theta_{2}$ with respect to the initial direction of motion of the body of mass $M$. The largest possible value of the ratio $M/m$,for which the angles $\theta_{1}$ and $\theta_{2}$ will be equal,is:

Derive the expressions for the velocities of two bodies after a one-dimensional elastic collision.

$A$ ball after falling from a height of $10\, m$ strikes the roof of a lift which is descending down with a velocity of $1\, m/s$. The recoil velocity of the ball will be .............. $m/s$.

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?