$A$ 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. $......^{\circ}$

The bob $A$ of a pendulum,released from a horizontal position to the vertical,hits another bob $B$ of the same mass at rest on a table as shown in the figure. If the length of the pendulum is $1\,m$,calculate:
$(a)$ The height to which bob $A$ will rise after the collision.
$(b)$ The speed with which bob $B$ starts moving.
Neglect the size of the bobs and assume the collision to be elastic.

$A$ sphere of mass $m$,moving with velocity $3u$,collides head-on with another identical sphere at rest. If $e$ is the coefficient of restitution,what will be the ratio of the velocity of the second sphere to that of the first sphere after the collision?

$A$ body of mass $2\,kg$ makes an elastic collision with a second body of mass $m$ at rest and continues to move in the original direction but with one-fourth of its original speed. What is the mass of the second body? ................ $kg$

$A$ particle of mass $m$,moving with a velocity $v$,makes an elastic collision in one dimension with a stationary particle of mass $m$. During the collision,they remain in contact with each other for an extremely small time $T$. Their force of contact with time is shown in the figure. Then $F_0 =$

$A$ moving body with mass $m_1$ strikes a stationary mass $m_2$. What should be the ratio $\frac{m_1}{m_2}$ so as to decrease the velocity of the first body by $1.5$ times after the collision?