$A$ body falls from a height of $10 \ m$ onto the ground and rebounds to a height of $2.5 \ m$. The percentage loss in kinetic energy is ......... $\%$.

$A$ cricket ball hits the ground with a speed of $5 \,m \,s^{-1}$ making an angle of $30^{\circ}$ with the horizontal. If the coefficient of restitution is $0.2$, the speed of the reflected ball in $m \,s^{-1}$ is

$A$ small steel ball bounces on a steel plate held horizontally. On each bounce,the speed of the ball arriving at the plate is reduced by a factor $e$ (coefficient of restitution) in the rebound,so that $V_{\text{upward}} = e V_{\text{downward}}$. If the ball is initially dropped from a height of $0.4 \text{ m}$ above the plate and if $10 \text{ s}$ later the bouncing ceases,the value of $e$ is:

Two pendulums with identical bobs and lengths are suspended from a common support such that in rest position the two bobs are in contact (figure). One of the bobs is released after being displaced by $10^{\circ}$ so that it collides elastically head-on with the other bob.
$(a)$ Describe the motion of two bobs.
$(b)$ Draw a graph showing variation in energy of either pendulum with time,for $0 \leqslant t \leqslant 2T$,where $T$ is the period of each pendulum.

$A$ 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 falls vertically onto a floor with momentum $p$ and then bounces repeatedly. If the coefficient of restitution is $e$, then the total momentum imparted by the ball on the floor is: