$A$ $1.0 \ kg$ ball drops vertically onto a floor from a height of $25 \ cm$. It rebounds to a height of $4 \ cm$. The coefficient of restitution for the collision is

$A$ particle of mass $m$ collides with another stationary particle of mass $M$. The particle of mass $m$ stops just after the collision. 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

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.

$A$ bullet of mass $m$ and speed $v$ hits a pendulum bob of mass $M$ at time $t_1$,and passes completely through the bob. The bullet emerges at time $t_2$ with a speed of $v/2$. The pendulum bob is suspended by a stiff rod of length $l$ and negligible mass. After the collision,the bob can barely swing through a complete vertical circle. At time $t_3$,the bob reaches the highest position. What quantities are conserved in this process?

$A$ ball impinges directly on a similar ball of same mass at rest. If $1/4$ of the kinetic energy is lost by the impact,the value of the coefficient of restitution is