$A$ sphere of mass $M$ moving with velocity $u$ undergoes a perfectly elastic head-on collision with another sphere of mass $m$ at rest. After the collision,their velocities are $V$ and $v$ respectively. Find the value of $v$.

$A$ perfectly rigid billiard ball of kinetic energy $E_k$ collides with an identical stationary ball. After the collision,the kinetic energy of the first ball becomes $E'_k$. Then,which of the following is true?

$A$ 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:

$A$ ball of mass $m$ suspended from a rigid support by an inextensible massless string is released from a height $h$ above its lowest point. At its lowest point, it collides elastically with a block of mass $2m$ at rest on a frictionless surface. Neglect the dimensions of the ball and the block. After the collision, the ball rises to a maximum height of

$A$ block having mass $m$ collides with another stationary block having mass $2m$. The lighter block comes to rest after the collision. If the initial velocity of the first block is $v$,then the value of the coefficient of restitution must be:

The bob $A$ of a simple pendulum is released when the string makes an angle of $45^o$ with the vertical. It hits another bob $B$ of the same material and same mass kept at rest on the table. If the collision is elastic,then