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

Question

A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with the speed of 0.5 m s- 1 . What is the height of the plane of the circle from the vertex of the funnel? (A) 0.25 cm (B) 2 cm (C) 4 cm (D) 2.5 cm

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-dirqpppjc4xb.png" /> Nsin θ =mg Ncos θ =m v2 / r Dividing above equations ⇒ tan θ =r g / v2 ⇒ (r/h)=(r g/v2) ⇒ h=(v2/g)=2.5 cm

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

$0.25 c m$

$2 c m$

$4 c m$

$2.5 c m$

$N s in θ = m g$
$N cos θ = m v^{2} / r$
Dividing above equations
$\Rightarrow t an θ = r g / v^{2}$
$\Rightarrow \frac{r}{h} = \frac{r g}{v ^{2}}$
$\Rightarrow h = \frac{v ^{2}}{g} = 2.5 c m$

Q. A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with the speed of 0.5ms−1 . What is the height of the plane of the circle from the vertex of the funnel?

0.25cm

2cm

4cm

2.5cm