A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with spee

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3-2.Motion in Plane

hard

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

A$0.25$

B$2 $

C$4$

D$2.5 $

Solution

(d) The particle is moving in circular path
From the figure, $mg = R\sin \theta $ …$(i)$
$\;\frac{{m{v^2}}}{r} = R\cos \theta $ …$(ii)$
From equation $(i)$ and $(ii)$ we get
$\tan \theta = \frac{{rg}}{{{v^2}}}$ but $\tan \theta = \frac{r}{h}$
$h = \frac{{{v^2}}}{g} = \frac{{{{(0.5)}^2}}}{{10}} = 0.025m = 2.5\,cm$

Standard 11

Physics

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