JEE Main · 2021 · 26 Aug 2021 · Shift 2 · Laws of Motion

A particle of mass

m

is suspended form a ceiling through a string of length

L

. The particle moves in a horizontal circle of radius

r

such that

r = \frac{L}{2}

. The speed of particle will be:

(A) $rg$ ✓ Correct
(B) $\frac{r g}{2}$
(C) $2 rg$
(D) $2 r g$

Answer: (A)

Solution

The string makes an angle

θ

with the vertical, and the radius of the circle is

r = L sin θ

, so

sin θ = \frac{r}{L} = \frac{1}{2}

and

θ = 4 5^{\circ}

.
The vertical component of the tension balances the weight while the horizontal component supplies the centripetal force:

T cos θ = m g, T sin θ = \frac{m v ^{2}}{r}

Dividing one by the other gives

tan θ = \frac{v ^{2}}{r g}

. With

tan 4 5^{\circ} = 1

, the speed is

v = r g

JEE Main · 2021 · 26 Aug 2021 · Shift 2 · Single correct option

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