$A$ 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 $\text{ cal}$)

$A$ small ball falling vertically downward with a constant velocity of $4 \ m/s$ strikes elastically a massive inclined cart moving with a velocity of $4 \ m/s$ horizontally,as shown in the figure. The velocity of the rebound of the ball is

$A$ ball of mass $M$ falls from a height $h$ on a floor. If the coefficient of restitution is $e$,the height attained by the ball after two rebounds is

$A$ ball falls freely from a height $h$ on a rigid horizontal plane. If the coefficient of restitution is $e$,then the total distance travelled by the ball before hitting the plane the second time is

An inelastic ball is dropped from a height of $100\, m$. Due to the impact,$20\%$ of its energy is lost. To what height will the ball rise?

$A$ mass $m$ moves with a velocity $v$ and collides inelastically with another identical mass at rest. After the collision,the $1^{st}$ mass moves with velocity $\frac{v}{\sqrt{3}}$ in a direction perpendicular to the initial direction of motion. Find the speed of the $2^{nd}$ mass after the collision.