A ball is thrown with a velocity of $6\, m/s$ vertically downwards from a height $H = 3.2\, m$ above a horizontal floor. If it rebounds back to same height then coefficient of restitution $e$ is $[g = 10\, m/s^2]$

A ball of $0.4\,kg$ mass and a speed of $3\, m/s$ has a head-on, completely elastic  collision with a $0.6-kg$ mass initially at rest. Find the speeds of both balls after the  collision:

In $a$ one-dimensional collision, $a$ particle of mass $2m$ collides with $a$ particle of mass $m$ at rest. If the particles stick together after the collision, what fraction of the initial kinetic energy is lost in the collision?

Two balls $A$ and $B$ having masses $1\, kg$ and $2\, kg$, moving with speeds $21\, m/s$ and $4\, m/s$ respectively in opposite direction, collide head on. After collision Amoves with a speed of $1\,m/s$ in the same direction, then correct statements is :

Two particles of equal mass $\mathrm{m}$ have respective initial velocities $u\hat{i}$ and $u\left(\frac{\hat{\mathrm{i}}+ \hat{\mathrm{j}}}{2}\right) .$ They collide completely inelastically. The energy lost in the process is

A billiard ball moving with a speed of $5 \,m/s$ collides with an identical ball originally at rest. If the first ball stops after collision, then the second ball will move forward with a speed of ...........  $m{s^{ - 1}}$