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:

Two identical spheres move in opposite directions with speeds $v_1$ and $v_2$ and pass behind an opaque screen, where they may either cross without touching (Event $1$) or make an elastic head-on collision (Event $2$)

A dumbbell consisting of two masses $m$ each, connected by a light rigid rod of length $l$, falls on two pads of equal height, one steel and the other brass through a height $h$. The coefficient of restitution are $e_1$ and $e_2$ ($e_1 < e_2$). To what maximum height will the centre of mass of the dumbbell rise after bouncing of the pads?

A ball after falling from a height of  $10\,\,m$  strikes the roof of a lift which is descending down with a velocity of  $1\,\,m/s$ . The recoil velocity of the ball will be ............. $\mathrm{m}/ \mathrm{s}$

A particle of mass $m$ is moving with speed $2\, v$ collides with a mass $2\,m$ moving with speed $v$ in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass $m$, which move at angle $45^o$ with respect to the original direction. The speed of each of the moving particle will be

Ball $A$ moving at $12\  m/s$ collides elastically with $B$ as shown. If both balls have the same mass, what is the final velocity of ball $A$ ? ................$m/s$