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?

Question

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? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-mydqpnnhfvmn.png" /> Nsin θ =mg Ncos θ =mv2/r Dividing above equations ⇒ tan θ =rg/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 a speed of $0.5 m s^{- 1}$ . What is the height (in $c m$ ) of the plane of the circle from the vertex of the funnel?

$N s in θ = m g$
$N cos θ = m v^{2} / r$
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 a speed of 0.5ms−1 . What is the height (in cm ) of the plane of the circle from the vertex of the funnel?

Nsinθ=mg Ncosθ=mv2/r Dividing above equations ⇒tanθ=rg/v2 ⇒hr​=v2rg​ ⇒h=gv2​=2.5cm

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 $c m$ ) of the plane of the circle from the vertex of the funnel?

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