Question

A small steel ball A is suspended by an inextensible thread of length $l=15m$ from O. Another identical ball is thrown vertically downwards such that its surface remains just in contact with thread during downward motion and collides elastically with the suspended ball. If the suspended ball just completes vertical circle after collision, calculate the velocity (in cm/s) of the falling ball just before collision : $(g=10m{s}^{-2})$

Answer 1

Since the ball just completes a vertical circle, it must have a velocity of $\sqrt{5gl}$

From geometry, the angle between vertical and line of collision between the balls is ${30}^{\circ }$

Thus, from conservation of momentum of both the balls and the condition of elasticity,

velocity of ball A along the horizontal direction after collision $=0.8v_0\cos {30}^{\circ }=\sqrt{5gl}$

$⟹v_0=12.5m/s$