Question

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

• A. $0.25\text{cm}$
• B. $2\text{cm}$
• C. $0.025\text{cm}$
• D. $2.5\text{cm}$

Answer 1

The correct option is D $2.5\text{cm}$


$N\cos \theta =\frac{m{v}^2}{R}$
$N\sin \theta =mg$
$\tan \theta =\frac{gR}{v^2}$
$\frac{R}{h}=\frac{gR}{v^2}$
$h=\frac{v^2}{g}=\frac{0.5\times 0.5}{10}=0.025\text{m}.$