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

Two identical balls $A$ and $B$ having velocities of $0.5\, m s^{-1}$ and $-0.3 \, m s^{-1}$ respectively collide elastically in one dimension. The velocities of $B$ and $A$ after the collision respectively will be

A mass $'m'$ moves with a velocity $'v'$ and collides inelastically with another identical mass. After collision the $1^{st}$ mass moves with velocity $\frac{v}{{\sqrt 3 }}$ in a direction perpendicular to the initial direction of motion. Find the speed of the $ 2^{nd}$ mass after collision

A ball of mass $10\, kg$ moving with a velocity $10 \sqrt{3}\, ms ^{-1}$ along $X-$axis, hits another ball of mass $20\, kg$ which is at rest. After collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along $Y-$ axis at a speed of $10\, m / s$. The second piece starts moving at a speed of $20\, m / s$ at an angle $\theta$ (degree) with respect to the $X-$axis. The configuration of pieces after collision is shown in the figure. The value of $\theta$ to the nearest integer is

Three objects $A, B$ and $C$ are kept in a straight line on a frictionless horizontal surface. The masses of ${A}, {B}$ and ${C}$ are ${m}, 2\, {m}$ and $2\, {m}$ respectively. $A$ moves towards ${B}$ with a speed of $9$ ${m} / {s}$ and makes an elastic collision with it. Thereafter $B$ makes a completely inelastic collision with $C.$ All motions occur along same straight line. The final speed of $C$ is $....\,{m} / {s}$

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