Kinematics

JEE Main level, single correct, medium

284 of 308

Question 284 of 308

A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius 9 m9 \mathrm{~m} and completes 120 resolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is (\left(\right. in m/s2\mathrm{m} / \mathrm{s}^2 ) :

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Answer: (D) 16π2 ms−216 \pi^2 \mathrm{~ms}^{-2}

 Given : R=9 m,120 revolution in 3 minω=120Rev.3 min.=120×2πrad3×60sec=4π3rad/sacentripetal =ω2R=(4π3)2×9=16π2 m/s2\begin{aligned} & \text { Given : } \mathrm{R}=9 \mathrm{~m}, \\ & 120 \text { revolution in } 3 \mathrm{~min} \\ & \omega=\frac{120 \mathrm{Rev} .}{3 \mathrm{~min} .}=\frac{120 \times 2 \pi \mathrm{rad}}{3 \times 60 \mathrm{sec}}=\frac{4 \pi}{3} \mathrm{rad} / \mathrm{s} \\ & \mathrm{a}_{\text {centripetal }}=\omega^2 \mathrm{R}=\left(\frac{4 \pi}{3}\right)^2 \times 9=16 \pi^2 \mathrm{~m} / \mathrm{s}^2\end{aligned}

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