Question

A point mass can slide in a vertical plane on a frictionless curvilinear track as shown in the figure. Sections $AB$ and $BC$ of the track are circular arcs each of angular span ${120}^{\circ }$ and radius $r$. From what minimum height above the bottom of section $AB$ should a small block $P$ be released so that it certainly loses contact with the track?

Answer 1

$Mass=m$

AB,BC. angular Spam $120°$

Radius $=r$

$h=mr\cos 120°\cos 60°=mr\sin (180°-60°)=mr\frac{1}{2}=\frac{1}{2}mr$