JEE Main · 2024 · 05 Apr 2024 · Shift 2 · Kinematics

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A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius 9 m and completes 120 revolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is (in

m / s^{2}

) :

(A)zero
(B) $16 π^{2} ms^{- 2}$ ✓ Correct
(C) $4 π^{2} ms^{- 2}$
(D) $57600 π^{2} ms^{- 2}$

Answer: (B)

Solution

Angular speed of the cyclist (and hence of the monkey, since both move on the same circular path):

ω = \frac{120 \times 2 π}{3 \times 60} = \frac{4 π}{3} rad/s

Centripetal acceleration, with

R = 9

a = ω^{2} R = (\frac{4 π}{3})^{2} (9) = \frac{16 π ^{2}}{9} \times 9 = 16 π^{2} m/s^{2}

JEE Main · 2024 · 05 Apr 2024 · Shift 2 · Single correct option

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