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?

$A$ body moving with velocity $v$ has momentum and kinetic energy numerically equal. What is the value of $v$ in $m/s$?

In the diagram shown,there is no friction at any contact surface. Initially,the spring has no deformation. What will be the maximum deformation in the spring? Consider all the strings to be sufficiently large. Consider the spring constant to be $K$.

$A$ block of mass $m$ slides from rest at a height $H$ on a frictionless inclined plane as shown in the figure. It travels a distance $d$ across a rough horizontal surface with coefficient of kinetic friction $\mu$ and compresses a spring of spring constant $k$ by a distance $x$ before coming to rest momentarily. Then the spring extends and the block travels back attaining a final height of $h$. Then,

$A$ bullet of mass $25 \,g$ moving horizontally at a speed of $250 \,m/s$ is fired into a wooden block of mass $1 \,kg$ suspended by a long string. The bullet crosses the block and emerges on the other side. If the centre of mass of the block rises through a height of $20 \,cm$, find the speed of the bullet as it emerges from the block. (Take $g = 10 \,m/s^2$) (in $\,m/s$)

Underline the correct alternative:
$(a)$ When a conservative force does positive work on a body,the potential energy of the body increases/decreases/remains unaltered.
$(b)$ Work done by a body against friction always results in a loss of its kinetic/potential energy.
$(c)$ The rate of change of total momentum of a many-particle system is proportional to the external force/sum of the internal forces on the system.
$(d)$ In an inelastic collision of two bodies,the quantities which do not change after the collision are the total kinetic energy/total linear momentum/total energy of the system of two bodies.