JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Laws of Motion

A car is moving with a constant speed of 20

m / s

in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take

g = 10 m / s^{2}

)

(A) $\frac{π}{6}$
(B) $\frac{π}{2}$
(C) $\frac{π}{4}$ ✓ Correct
(D) $\frac{π}{3}$

Answer: (C)

Solution

A bob hanging in a car that rounds a horizontal circle settles so the string tension balances gravity vertically and supplies the centripetal force horizontally:

T cos θ = m g

and

T sin θ = \frac{m v ^{2}}{R}

. Dividing,

tan θ = \frac{v ^{2}}{R g} = \frac{2 0 ^{2}}{40 \times 10} = 1

. The string makes an angle

θ = \frac{π}{4}

with the vertical.

JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Single correct option

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