$A$ ball initially at rest is hit by another identical ball moving with some velocity as shown. Find the angle $\theta_2$ if the surface is without friction and the collision is perfectly elastic. $......^{\circ}$

$A$ block having mass $m$ collides with another stationary block having mass $2m$. The lighter block comes to rest after the collision. If the initial velocity of the first block is $v$,then the value of the coefficient of restitution must be:

Two masses $m_1$ and $m_2$ moving with velocities $v_1$ and $v_2$ in opposite directions collide elastically and after collision masses $m_1$ and $m_2$ move with velocity $v_2$ and $v_1$ respectively. The ratio $\left(\frac{m_2}{m_1}\right)$ is

In the figure,determine the type of collision. The masses of the blocks,and the velocities before and after the collision are given. The collision is

Explain the special cases of elastic collision in one dimension.

$A$ steel ball of radius $2 \,cm$ is at rest on a frictionless surface. Another steel ball of radius $4 \,cm$ moving with velocity of $81 \,cm \,s^{-1}$ collides elastically with the ball which is at rest. After collision, the ball with radius of $2 \,cm$ moves with a speed of: