$A$ body falls freely onto a hard horizontal surface. If the coefficient of restitution between the surface and the body is $e = 0.8$,then the ratio of the maximum height to which the body rises after the second impact to the initial height of the body 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

$A$ ball moving with a velocity of $9 \ m/s$ collides with another similar stationary ball. After the collision,both balls move in directions making an angle of $30^{\circ}$ with the initial direction. After the collision,their speed will be $-$

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.

$A$ ball of mass $2 \ g$ moving with a velocity of $2 \ ms^{-1}$ collides with another ball of mass $8 \ g$ which is at rest and comes to rest after collision. Then the coefficient of restitution is

$A$ body falls freely from a height of $100 \ m$ onto the ground and rebounds to a maximum height of $36 \ m$ after collision. The coefficient of restitution between the ground and the body is