JEE Mains · Physics · STD 11 - Motion in plane
- JEE Mains 2024
- Hard
- MCQ
A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius \(9 \mathrm{~m}\) and completes \(120\) revolutions in \(3\) minutes. The magnitude of centripetal acceleration of monkey is _______ (in \(\mathrm{m} / \mathrm{s}^2\) ).
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(16 \pi^2 \mathrm{~ms}^{-2}\)
Step-by-step Solution
Detailed explanation
\(\text { Given : } R=9 \mathrm{~m},\)
\(120 \text { revolution in } 3 \mathrm{~min}\)
\(\omega=\frac{120 \mathrm{Rev}}{3 \mathrm{~min} .}=\frac{120 \times 2 \pi \mathrm{rad}}{3 \times 60 \mathrm{sec}}=\frac{4 \pi}{3} \mathrm{rad} / \mathrm{s}\)
\(\mathrm{a}_{\text {centripetal }}=\omega^2 \mathrm{R}=\left(\frac{4 \pi}{3}\right)^2 \times 9=16 \pi^2 \mathrm{~m} / \mathrm{s}^2\)
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