A particle originally at rest at the highest point of a smooth vertical circle is slightly displaced. It will leave the circle at a vertical distance $h$ below the highest point such that
A particle originally at rest at the highest point of a smooth vertical circle is slightly displaced. It will leave the circle at a vertical distance $h$ below the highest point such that
$h = R$
$h = \frac{R}{3}$
$h = \frac{R}{2}$
$h = \frac{{2R}}{3}$
A particle originally at rest at the highest point of a smooth vertical circle is slightly displaced. It will leave the circle at a vertical distance $h$ below the highest point such that
$h=R-R \cos \theta, v=\sqrt{2 g h}=\sqrt{2 g R(1-\cos \theta)}$
$m g \cos \theta-N=\frac{m v^{2}}{R}$
When it leaves circle: $N=0$ $m g \cos \theta=\frac{m v^{2}}{R} \Rightarrow \cos \theta=\frac{2}{3}$
$h=R-R \cos \theta=\frac{R}{3}$