Statement-1: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.

Statement-2: Principle of conservation of momentum holds true for all kinds of collisions.

A ball of mass $0.2 \mathrm{kg}$ rests on a vertical post of height $5 \mathrm{m}$. A bullet of mass $0.01 \mathrm{kg}$, travelling with a velocity $V \mathrm{m} {\mathrm{s}}^{-1}$ in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of $20 \mathrm{m}$ and the bullet at a distance of $100$ $\mathrm{m}$ from the foot of the post. The initial velocity $V$ of the bullet is

This question has $Statement\; -\; I$ and $Statement\; -\; II$ of the four choices given after the Statements, choose the one that best describes the two Statements.

$Statement\; -\; I:$ A point particle of mass $m$ moving with speed $\nu$ collides with stationary point particle of mass $M$. If the maximum energy loss possible is given as
$f\left(\frac{1}{2}m{\nu }^2\right)$ then $f=\left(\frac{m}{M+m}\right)$.

$Statement\; -\; II:$ Maximum energy loss occurs when the particles get stuck together as a result of the collision.

Three blocks$A, B$ and $C$ are lying on a smooth horizontal surface, as shown in the figure. $A$ and $B$ have equal masses, $m$ and $C$ has mass $M$. Block $A$ is given an initial speed $v$ towards $B$ due to which it collides with $B$ perfectly inelastically. The combined mass collides with $C$, also perfectly inelastically. $\frac{5}{6}$$\mathrm{th}$ of the initial kinetic energy is lost in the whole process. What is value of $\frac{M}{m}$ ?