$A$ sphere of mass $m$ moving with velocity $u$ undergoes a collision with a stationary sphere of mass $m$. If the coefficient of restitution is $e = 1/2$,what is the ratio of the final velocities of the two spheres?

$A$ particle falls from a height $h$ on a static horizontal plane and rebounds. If $e$ is the coefficient of restitution,then the total distance traveled by the particle before coming to rest will be:

$A$ 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 $g = 10\, m/s^2$)

$A$ 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:

$A$ moving ball collides head-on with a similar ball at rest. If $\frac{1}{4}$ of the kinetic energy is lost during the impact,the value of the coefficient of restitution is:

$A$ ball falls from a height $h$ and rebounds after striking the floor. The coefficient of restitution is $e$. The total distance covered by the ball before it comes to rest is