$A$ ball initially at rest is hit by another identical ball moving with some velocity as shown. Find the angle $\theta_2$ if the surface is without friction and the collision is perfectly elastic. $......^{\circ}$

$Assertion$: $n$ small balls each of mass $m$ collide elastically each second on a surface with velocity $u$. The force experienced by the surface is $2mnu$.
$Reason$: On elastic collision,the ball rebounds with the same velocity.

In an elastic collision of two particles,which of the following quantities is conserved?

$A$ ball of mass $2m$ and a system of two balls with equal masses $m$ connected by a massless spring are placed on a smooth horizontal surface (see figure). Initially, the ball of mass $2m$ moves with velocity $u_0$ along the line passing through the centres of all the balls and the spring, whereas the system of two balls is at rest. Assuming that the collision between the individual balls is perfectly elastic, the ratio of vibrational energy stored in the system of two connected balls to the initial kinetic energy of the ball of mass $2m$ is

Assertion $(A)$: In an elastic collision between two bodies,the relative speed of the bodies after collision is equal to the relative speed before the collision.
Reason $(R)$: In an elastic collision,the linear momentum of the system is conserved.

$A$ body of mass $m$ moving with velocity $u_1$ collides elastically with another body of the same mass $m$ at rest. After the collision,they move at an angle of .............. $^o$ to each other.