Five identical elastic balls are suspended in a row with strings of equal length such that the distance between the sides of the balls is very small. If the ball at the right end is released from one side,then:

$A$ ball of mass $0.1 \ kg$ undergoes a head-on collision with a stationary ball of unknown mass. If the $0.1 \ kg$ ball rebounds with $1/3$ of its original speed,the mass of the second ball is .......... $kg$.

$A$ ball of mass $m$ moving with speed $v$ collides elastically with an identical stationary ball which is initially at rest. After collision,the first ball moves at an angle $\theta$ to its initial direction and has speed $(v/3)$. The second ball moves in a straight line after the collision. Then,the speed of the second ball after the collision is:

$A$ body of mass $1\,kg$ collides head-on elastically with a stationary body of mass $3\,kg$. After the collision,the smaller body reverses its direction of motion and moves with a speed of $2\,m/s$. The initial speed of the smaller body before the collision is $..........\,m/s$.

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:

There are $n$ elastic balls placed on a smooth horizontal plane. The masses of the balls are $m, \frac{m}{2}, \frac{m}{2^2}, \ldots, \frac{m}{2^{n-1}}$ respectively. If the first ball hits the second ball with velocity $v_0$, then the velocity of the $n^{\text{th}}$ ball will be,