$A$ ball of mass $10 \text{ g}$ is allowed to fall from a height of $10 \text{ m}$. After the collision with the ground, if $50\%$ of its energy is lost, then the height reached by the ball is: (in $\text{ m}$)

$A$ 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:

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

$A$ 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?

$A$ body falls on a surface of coefficient of restitution $0.6$ from a height of $1 \ m$. Then the body rebounds to a height of (in $m$)

$A$ ball with a speed of $9\, m/s$ collides with another identical ball at rest. After the collision,the direction of each ball makes an angle of $30^{\circ}$ with the original direction. The ratio of velocities of the balls after collision is $x : y$ where $x$ is........