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,

Two blocks $A$ and $B$ of masses $m$ and $2m,$ respectively, are connected with the help of a spring having a spring constant, $k$ as shown in the figure. Initially, both the blocks are moving with the same velocity, $v$ on a smooth horizontal plane with the spring in its natural length. During their course of motion, block, $B$ makes an inelastic collision with block, $C$ of mass $m$ which is initially at rest. The coefficient of restitution for the collision is $\frac{1}{2}$. The maximum compression in the spring is, 

Three blocks are initially placed as shown in the figure. Block-$A$ has mass $\text{'}m\text{'}$ and initial velocity $v$ to the right. Block-$B$ with mass $\text{'}m\text{'}$ and block- $C$ with mass $4m$ are both initially at rest. Neglect friction. All collisions are elastic. The final velocity of block - $A$ is :-

In the figure shown, the two identical balls of mass, $M$ and radius, $R$ each, are placed in contact with each other on the frictionless horizontal surface. The third ball of mass, $M$ and radius $\frac{R}{2}$, is coming down vertically and has a velocity $=v_0$ when it simultaneously hits the two balls and itself comes to rest. Then, each of the two bigger balls will move after collision with a speed equal to