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?

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? (A) 0.25 cm (B) 2 cm (C) 4 cm (D) 2.5 cm

Tardigrade Admin · Accepted Answer

The particle is moving in circular path

From the figure,

m g = R s in θ \dots (i)

\frac{m v ^{2}}{r} = R cos θ \dots (ii)

From equation (i) and (ii) we get

t an θ = \frac{r g}{v ^{2}}

but

t an θ = \frac{r}{h}

∴ h = \frac{v ^{2}}{g} = \frac{( 0.5 ) ^{2}}{10}

= 0.025 m = 2.5 c m

Q. 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?

$0.25 c m$

$2 c m$

$4 c m$

$2.5 c m$

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

0.25cm

2cm

4cm

2.5cm

The particle is moving in circular path From the figure, mg=Rsinθ…(i) rmv2​=Rcosθ…(ii) From equation (i) and (ii) we get tanθ=v2rg​ but tanθ=hr​ ∴h=gv2​=10(0.5)2​ =0.025m=2.5cm

Q. 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?

$0.25 c m$

$2 c m$

$4 c m$

$2.5 c m$