$A$ sphere strikes a wall and rebounds with a coefficient of restitution $e = 1/3$. If it rebounds with a velocity of $0.1 \ m/s$ at an angle of $60^{\circ}$ to the normal to the wall,the percentage loss of kinetic energy is:

$A$ ball is dropped from a height $h$ on a floor of coefficient of restitution $e$. The total distance covered by the ball just before the second hit is

$A$ body moving along a straight line collides with another body of the same mass moving in the same direction with half of the velocity of the first body. If the coefficient of restitution between the two bodies is $0.5$,then the ratio of the velocities of the two bodies after collision is (treat the collision as one dimensional).

$A$ ball moving with velocity $2 \,m/s$ collides head-on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$, then their velocities (in $m/s$) after collision will be:

$A$ particle of mass $m_1$ moving along the $X$-axis collides with a stationary particle of mass $m_2$ and deviates by an angle $30^{\circ}$ to the $X$-axis as shown in the figure. If the percentage change in kinetic energy of the combined system of these two particles reduces by $50 \%$,then the ratio of the masses $\frac{m_2}{m_1}$ 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.