Question

A particle describes a horizontal circle of radius $r$ on the smooth surface of an inverted cone as shown. The height of plane of circle above vertex is $h$. The speed of particle should be

• A. $\sqrt{rg}$
• B. $\sqrt{2rg}$
• C. $\sqrt{gh}$
• D. $\sqrt{2gh}$

Answer 1

The correct option is C $\sqrt{gh}$

$Ncos\theta =mgNsin\theta =\frac{{mv}^2}{r}tan\theta =\frac{v^2}{rg}nowtan\theta =\frac{h}{r}\frac{h}{r}=\frac{v^2}{rg}v=\sqrt{hg}$