$A$ ball is moving with speed $20 \, m/s$ collides with a smooth surface as shown in the figure. The magnitude of the change in velocity of the ball will be ........... $m/s$.

$A$ ball is let fall from a height $h_0$. It makes $n$ collisions with the earth. After $n$ collisions it rebounds with a velocity $v_n$ and the ball rises to a height $h_n$,then the coefficient of restitution is given by

$A$ body is dropped on the ground from a height $h_1$ and after hitting the ground,it rebounds to a height $h_2$. If the ratio of velocities of the body just before and after hitting the ground is $4$,then the percentage loss in kinetic energy of the body is $\frac{x}{4}$. The value of $x$ is $.......$

The sphere $A$ of mass $m$ moving with a constant velocity hits another sphere $B$ of mass $2m$ at rest. If the coefficient of restitution is $0.4$,the ratio of the velocities of the spheres $A$ and $B$ after collision is

Two particles of masses $m_1$ and $m_2$ move with initial velocities $u_1$ and $u_2$. On collision,one of the particles gets excited to a higher level after absorbing energy $\varepsilon$. If the final velocities of the particles are $v_1$ and $v_2$,then we must have:

$A$ bullet of mass $4.2 \times 10^{-2} \text{ kg}$, moving at a speed of $300 \text{ m/s}$, gets stuck into a block with a mass $9$ times that of the bullet. If the block is free to move without any kind of friction, the heat generated in the process will be (in $\text{ cal}$)