$A$ body of mass $m$ moving with velocity $v$ collides head-on with another body of mass $2m$ which is initially at rest. The ratio of the $K.E.$ of the colliding body before and after the collision will be: (in $: 1$)

$A$ sphere of mass $M$ moving with velocity $u$ undergoes a perfectly elastic head-on collision with another sphere of mass $m$ at rest. After the collision,their velocities are $V$ and $v$ respectively. Find the value of $v$.

$A$ particle of mass $m$ moving with velocity $v$ makes a perfectly elastic collision with a simple pendulum bob of mass $m$. After the collision,the maximum height attained by the bob is:

$A$ ball falls from a height of $5\,m$ and strikes the roof of a lift. If at the time of collision,the lift is moving in the upward direction with a velocity of $1\,m/s$,then the velocity with which the ball rebounds after collision will be (assume $e = 1$):

Two equal masses $m_1$ and $m_2$ moving along the same straight line with velocities $+3 \, m/s$ and $-5 \, m/s$ respectively collide elastically. Their velocities after the collision will be respectively

$A$ billiard ball of mass $M$,moving with velocity $v_1$ collides with another ball of the same mass but at rest. If the collision is elastic,the angle of divergence after the collision is (in $^{\circ}$)