Q72 / 90 · JEE Main 2024 (05 Apr Shift 2) · Physics

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

  • A
    $57600 \pi^2 \mathrm{~ms}^{-2}$
  • B
    Zero
  • C
    $4 \pi^2 \mathrm{~ms}^{-2}$
  • Correct answer
    D
    $16 \pi^2 \mathrm{~ms}^{-2}$

Solution

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

Hence, the correct answer is option: 'D'.

Relevant Questions