A particle describes a horizontal circle in a conical funnel whose inner surface

Question

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?

Options:

A . 0.25 cm

B . 2 cm

C . 4 cm

D . 2.5 cm

Answer: Option D
:
D

A Particle Describes A Horizontal Circle In A Conical Funnel...

The particle is moving in circular path
From the figure, mg = Rsin

θ

..(i)

\frac{m v^{2}}{r}

= R cos

θ

..(ii)
From equation (i) and (ii) we get
tan

θ

\frac{r g}{v^{2}}

but tan

θ

\frac{r}{h}

∴

h =

\frac{v^{2}}{g}

\frac{{(0.5)}^{2}}{10}

= 0.025 m = 2.5 cm

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