Question

A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with the speed of $1 \, ms^{- 1}$ . What is the height (in $cm$ ) of the plane of the circle from the vertex of the funnel? $\left(g = 10 m s^{- 2}\right)$

Answer 1

$Nsin \theta =mg$
$Ncos \theta =m v^{2} / r$
Dividing above equations
$\Rightarrow \, tan \theta =r g / v^{2}$
$\Rightarrow \, \frac{r}{h}=\frac{r g}{v^{2}}$
$\Rightarrow \, h=\frac{v^{2}}{g}=10 \, cm$