Question

A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with the speed of $0.5 \, m \, s^{- 1}$ . What is the height of the plane of the circle from the vertex of the funnel?

• A. $0.25 \, cm$
• B. $2 \, cm$
• C. $4 \, cm$
• D. $2.5 \, cm$

Answer 1

Answer: (D)

$Nsin \theta =mg$
$Ncos \theta =m v^{2} / r$
Dividing above equations
$\Rightarrow \, tan \theta =r g / v^{2}$
$\Rightarrow \, \frac{r}{h}=\frac{r g}{v^{2}}$
$\Rightarrow \, h=\frac{v^{2}}{g}=2.5 \, cm$