$A$ 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

$A$ 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:

$A$ body falls from a height of $10 \ m$ onto the ground and rebounds to a height of $2.5 \ m$. Find the ratio of the velocity of the body just before the collision and just after the collision.

Two bodies having same mass $40\, kg$ are moving in opposite directions,one with a velocity of $10\, m/s$ and the other with $7\, m/s$. If they collide and move as one body,the velocity of the combination is ........ $m/s$.

Two solid rubber balls $A$ and $B$ having masses $200 \, g$ and $400 \, g$ respectively are moving in opposite directions. The velocity of $A$ is $0.3 \, m/s$. After the collision,both balls come to rest. Determine the velocity of $B$ in $m/s$.

$A$ rubber ball is released from a height of $5\, m$ above the floor. It bounces back repeatedly,always rising to $\frac{81}{100}$ of the height through which it falls. Find the average speed of the ball. (Take $g = 10\, m/s^2$)