The bob A of a pendulum released from horizontal 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 1m, 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.

When ball A reaches the bottom point its velocity is horizontal hene, we can apply conservation of linear momentum in the horizontal direction.

 
Hint: Apply conservation of linear momentum.
Step 1: Find the linear momentum of ball A just after the collision.

(a) Two balls have the same mass and collision between them is elastic, therefore, ball A transfers its entire linear momentum to ball B. Hence, ball A will come to rest after the collision and does not rise at all.

Step 2: Find speed of ball B just after the collision.

(b)Using linear momentum

Linear momentum of bob B just after collision = Linear momentum of bob A just before the collision.

As here masses of both balls are same 

So,

Speed with which bob B starts moving

= Speed with which bob A hits bob B=2gh=2×9.8×1=19.6=4.42m/s