Two balls of mass $5 \ kg$ are moving in opposite directions with the same speed of $5 \ m/s$. They undergo a head-on elastic collision. Find the final velocity of the balls in $m/s$.

When a moving body collides with a stationary body of $n$ times its mass,then the amount of kinetic energy transferred to the stationary body is

$A$ 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?

Two small particles of equal masses start moving in opposite directions from a point $A$ in a horizontal circular orbit. Their tangential velocities are $v$ and $2v$,respectively,as shown in the figure. Between collisions,the particles move with constant speeds. After making how many elastic collisions,other than that at $A$,will these two particles again reach the point $A$?

Given below are two statements. One is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$. Three identical spheres of same mass undergo one-dimensional motion as shown in the figure with initial velocities $v_{A} = 5 \ m/s$,$v_{B} = 2 \ m/s$,$v_{C} = 4 \ m/s$. If we wait sufficiently long for elastic collisions to happen,then $v_{A} = 4 \ m/s$,$v_{B} = 2 \ m/s$,$v_{C} = 5 \ m/s$ will be the final velocities.
Reason $(R)$: In an elastic collision between identical masses,two objects exchange their velocities. In the light of the above statements,choose the correct answer from the options given below:

$A$ billiard table has length and width as shown in the figure. $A$ ball is placed at point $A$. At what angle $\theta$ should the ball be projected so that after colliding with two walls,the ball will fall into the pocket $B$? Assume that all collisions are perfectly elastic and neglect friction.