$A$ 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 $v$.

$A$ ball $A$ of mass $m$ moving along the positive $x$-direction with kinetic energy $K$ and momentum $p$ undergoes an elastic head-on collision with a stationary ball $B$ of mass $M$. After the collision,the ball $A$ moves along the negative $x$-direction with kinetic energy $K/9$. The final momentum of $B$ is:

Two identical balls $A$ and $B$ having velocities of $0.5 \, m s^{-1}$ and $-0.3 \, m s^{-1}$ respectively collide elastically in one dimension. The velocities of $B$ and $A$ after the collision respectively will be

Consider an elastic collision of a particle of mass $m$ moving with a velocity $u$ with another particle of the same mass at rest. After the collision, the projectile and the struck particle move in directions making angles $\theta_1$ and $\theta_2$ respectively with the initial direction of motion. The sum of the angles, $\theta_1 + \theta_2$, is equal to: (in $^\circ$)

The bob of a simple pendulum (mass $m$ and length $l$) is dropped from a horizontal position. It strikes a block of the same mass $m$ placed on a horizontal frictionless table. The collision is elastic. The kinetic energy of the block after the collision will be

$A$ ball of mass $2 \,kg$ collides with another ball of mass $M$ at rest. If the collision is elastic and after the collision, the first ball moves with $\frac{1}{3}$ of its initial velocity in the same direction, then the mass of the second ball is: (in $\,kg$)