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  4. A particle describes a horizontal circle in a conical funnel, whose inner surface is smooth, with a speed of 0.5 m s- 1 . What is the height (in cm ) of the plane of the circle from the vertex of the funnel?

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

NTA AbhyasNTA Abhyas 2020Laws of Motion

Solution:

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