As shown in the figure,a pendulum $A$ is released from an angle of $30^{\circ}$ with the vertical and strikes a pendulum $B$ of equal mass. After the collision,to what height (in $m$) will pendulum $A$ rise? Neglect the size of the pendulum and assume the collision is perfectly elastic.

$A$ ball impinges directly on a similar ball at rest. If $1/4^{th}$ of the kinetic energy is lost by the impact, the value of the coefficient of restitution is:

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.

$A$ 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? ................ $kg$

$A$ body of mass $5\, kg$ moving with a velocity $10\, m/s$ collides with another body of mass $20\, kg$ at rest and comes to rest. The velocity of the second body due to the collision is ............ $m/s$.

$A$ ball of mass $m$ moving with velocity $v$ undergoes an elastic collision with another ball of the same mass $m$ moving in the opposite direction with velocity $2v$. What will be their velocities after the collision?