A metal ball falls from a height of $32$ metre on a steel plate. If the coefficient of restitution is $0.5$, to what height will the ball rise after second bounce ............ $m$

A dumbbell consisting of two masses $m$ each, connected by a light rigid rod of length $l$, falls on two pads of equal height, one steel and the other brass through a height $h$. The coefficient of restitution are $e_1$ and $e_2$ ($e_1 < e_2$). To what maximum height will the centre of mass of the dumbbell rise after bouncing of the pads?

A body falling from a height of $10\,m$ rebounds from hard floor. If it loses $20\%$ energy in the impact, then coefficient of restitution is

A train is moving at a constant speed $V$. When its driver observes another train in front of him on the same track and moving in the same direction with constant speed $u$. If the distance between the trains be $x$, then what should be the minimum retardation of the train so as to avoid collision?

$A$ chain of length $L$ and mass $m$ is placed upon a smooth surface. The length of $BA$ is $L-b$. Calculate the velocity of the chain when its end reaches $B$.

The friction coefficient between the horizontal surface and each of the block shown in  figure is $0.2.$ The collision between the blocks is perfectly elastic. What is the  separation between the blocks when they come to rest :- .............. $\mathrm{cm}$