A ball released from a height $h_0$ above a horizontal surface rebounds to a height $h_1$ after one bounce. The graph that relates $h_0$ to $h_1$ is shown in figure. If the ball (of the mass $\mathrm{m}$ ) was dropped from an initial height $h$ and made three bounces, the kinetic energy of the ball immediately after the third impact with the surface was

Two identical balls of equal masses $A$ and $B$ , are lying on a smooth surface as shown in the figure. Ball $A$ hits the ball $B$ (which is at rest) with a velocity $v=16\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$ . What should be the minimum value of coefficient of restitution $e$ebetween $A$ and $B$ so that $B$ just reaches the highest point of inclined plane. $\left(g=10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}\right)$

A ball of mass $m$ is released from rest relative to the elevator at a height $h_1$ above the floor of the elevator. After making a collision with the floor of the elevator it rebounds to height $h_2.$ The coefficient of restitution for collision is $e.$ For this situation, mark the correct statement(s).

A block of mass $\mathrm{m}$ starts from rest and slides down a frictionless semi-circular track from a height $h$ as shown. When it reaches the lowest point of the track, it collides with a stationary piece of putty also having mass $\mathrm{m}.$ If the block and the putty stick together and continue to slide, the maximum height that the block-putty

A particle of mass $\mathrm{m}$ comes down on a smooth inclined plane from point $B$ at a height of $h$ from rest. The magnitude of change in momentum of the particle between position $A$ (just before arriving on horizontal surface) and $C$ (assuming the angle of inclination of the plane as $\theta$ with respect to the horizontal) is

Three balls $A, B$ and $C$ of masses $2 \mathrm{kg}, 4 \mathrm{kg}$ and $8 \mathrm{kg},$ respectively, move along the same straight line and in the same direction, with velocities $4 \mathrm{m}/\mathrm{s}, 1 \mathrm{m}/\mathrm{s}$ and $3/4 \mathrm{m}/\mathrm{s}.$ If $A$ collides with $B$ and subsequently $B$ collides with $C,$ find the velocity of ball $A$ and ball $B$ after collision, taking the coefficient of restitution as unity.

Five balls are placed one after the other along a straight line as shown in the figure. Initially, all the balls are at rest. Then the second ball has been projected with speed $v_0$ towards the third ball. Mark the correct statements. (Assume all collisions to be head-on and elastic.)

A ball of mass $m$ is attached to a cord of length $L,$ pivoted at point $O,$ as shown in the figure. The ball is released from rest at point $A,$ swings down and makes an inelastic collision with a block of mass $2m$ kept on a rough horizontal floor. The coefficient of restitution of collision is, $e=\frac{2}{3}$, and coefficient of friction between block and surface is $\mu .$ After the collision, the ball comes momentarily to rest at $C$ when cord makes an angle of $\theta$ with the vertical and block moves a distance of, $\frac{3L}{2}$ on rough horizontal floor before stopping. The values of $\mu$ and $\theta$ are, respectively,