If a rubber ball falls from a height $h$ and rebounds up to a height of $h/2$,the percentage loss of total energy of the initial system and the velocity of the ball just before it strikes the ground,respectively,are:

If a skater of mass $3 \,kg$ has an initial speed of $32 \,m/s$ and a second skater of mass $4 \,kg$ has a speed of $5 \,m/s$. After a perfectly inelastic collision,they move together with a speed of $5 \,m/s$. Calculate the loss in kinetic energy.

For a collision between two particles,which of the following quantities is generally conserved?

$A$ ball is dropped vertically downwards from a height $h$ above the ground. It hits the ground inelastically and bounces up vertically. Neglecting subsequent motion and air resistance,which of the following graphs represents the variation between speed $(v)$ and height $(h)$ correctly?

$A$ 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,

$A$ 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 $\,m$)