$A$ particle of mass $m$ moving with a speed $v$ hits elastically another stationary particle of mass $2m$ in a fixed smooth horizontal circular tube of radius $R$. Find the time when the next collision will take place?

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:

Two equal masses $m_1$ and $m_2$ moving along the same straight line with velocities $+3 \, m/s$ and $-5 \, m/s$ respectively collide elastically. Their velocities after the collision will be respectively

$A$ particle of mass $m$ collides with another stationary particle of mass $M$. The particle $m$ stops just after the collision. The coefficient of restitution is:

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

Body $A$ of mass $4m$ moving with speed $u$ collides with another body $B$ of mass $2m$ at rest. The collision is head-on and elastic in nature. After the collision, the fraction of energy lost by the colliding body $A$ is: