$A$ mass $M$ moving with a certain speed $V$ collides elastically with another stationary mass $m$. After the collision,the masses $M$ and $m$ move with speeds $V^{\prime}$ and $v$,respectively. All motion is in one dimension. Then,

$A$ sphere of mass $10 \ kg$ moving with a velocity of $10 \ m/s$ undergoes an elastic collision with a body of mass $5 \ kg$ moving in the same direction with a velocity of $4 \ m/s$. What are their velocities after the collision?

$A$ body of mass $m$ moving with velocity $v$ makes a head-on elastic collision with another body of mass $2m$ which is initially at rest. What is the loss in kinetic energy of the colliding body?

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: Body $P$ having mass $M$ moving with speed $u$ has a head-on elastic collision with another body $Q$ having mass $m$ initially at rest. If $m << M$,body $Q$ will have a maximum speed equal to $2u$ after the collision.
Reason $R$: During an elastic collision,the momentum and kinetic energy are both conserved.
In the light of the above statements,choose the most appropriate answer from the options given below:

$A$ body of mass $4\ kg$ collides head-on elastically with another body of mass $2\ kg$ kept at rest in free space. The time of collision is $0.02\ s$ and the average impulsive force acting on each body is $100\ N$. Find the velocity of the $2\ kg$ body after the impact. (in $m/s$)

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