$A$ ball impinges directly on a similar ball at rest. If $1/4^{th}$ of the kinetic energy is lost by the impact, the value of the coefficient of restitution is:

$A$ ball of mass $1 \ kg$ moving along the $X$-direction collides elastically with a stationary ball of mass $m$. The first ball (mass $= 1 \ kg$) recoils at a right angle to its original direction of motion. If the second ball starts moving at an angle $30^{\circ}$ with the $X$-axis,the value of $m$ must be (in $kg$)

$A$ body of mass $2\,kg$ makes an elastic collision with a second body of mass $m$ at rest and continues to move in the original direction but with one-fourth of its original speed. What is the mass of the second body? ................ $kg$

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?

$STATEMENT-1$: In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. Because
$STATEMENT-2$: In an elastic collision, the linear momentum of the system is conserved.

Two billiard balls of mass $0.05\,kg$ each,moving in opposite directions with $10\,m/s$,collide and rebound with the same speed. If the time duration of contact is $t = 0.005\,s$,then the force exerted on the balls due to each other is $\dots N$.