Question

A small steel ball $A$ is suspended by an inextensible thread of length $l=1.5$ from $O$. Another indentical ball is thrown vertically downwards such that its surface remains just in contact with thread during downward motion and collides 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 of the falling ball just before collision.
$(g=10m{s}^{-2})$.

Answer 1

At time of collision velocity of $B$ along $OC$ is $v_0\cos 30°$.

After collision velocity along $\perp$ normal is interchanged.

${v=v}_0\cos 30°$

If $A$ complete verticle then $u=\sqrt{5gl}$

and $u=v_0\cos 60°=v_0\cos 30°\cos 60°=\sqrt{5gl}{v}_0\frac{\sqrt{3}}{2}\times \frac{1}{2}=\sqrt{5gl}{v}_0=4\sqrt{\frac{5}{3}gl}$