A particle is moving in a circle of radius $r$ under the action of a force $F=\alpha r^2$ which is directed towards centre of the circle. Total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy$=0$ for $r=0$):

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.

A ball of mass $100 \mathrm{g}$ is dropped from a height $h=10 \mathrm{cm}$ on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance $\frac{h}{2}$. The spring constant is _____ $\mathrm{N} {\mathrm{m}}^{-1}$
(Use $g=10{ \mathrm{m} \mathrm{s}}^{-2}$)