$A$ ball is released from a certain height. It loses $50\%$ of its kinetic energy on striking the ground. It will attain a height again equal to

$A$ simple pendulum of length $1 \,m$ has a wooden bob of mass $M = 1 \,kg$. It is struck by a bullet of mass $m = 10^{-2} \,kg$ moving with a speed of $u = 2 \times 10^2 \,m/s$. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is (use $g = 10 \,m/s^2$): (in $\,m$)

Two masses $m_1$ and $m_2$ are connected by a string of length $l$. They are held in a horizontal plane at a height $H$ above two heavy plates $A$ and $B$ made of different materials placed on the floor. Initially,the distance between the two masses is $a < l$. When the masses are released under gravity,they collide with $A$ and $B$ with coefficients of restitution $e_1 = 0.8$ and $e_2 = 0.4$ respectively. Find the time after the collision when the string becomes tight. (Assume $H >> l$)

$A$ body of mass $5 \,kg$ falls from a height of $30 \,m$. If all its mechanical energy is converted into heat,then the heat produced will be ........ $cal$.

Assertion $(A)$: When we bounce a ball on the ground, it comes to rest after a few bounces, losing all its energy. This is an example of violation of conservation of energy.
Reason $(R)$: Energy can change from one form to another but the total energy is always conserved.
Which of the following is true?

$A$ block of mass $m = 5 \text{ kg}$ is released from the top of an inclined plane as shown in the figure. The inclined plane has a length of $10 \text{ m}$ and an angle of $30^{\circ}$. The horizontal surface has a coefficient of kinetic friction $\mu = 0.5$ and a length of $2 \text{ m}$ before the spring of spring constant $k = 100 \text{ N/m}$. Calculate the maximum compression $x$ in the spring.