Q107 / 200 · NEET 2004 · Physics

A wheel having moment of inertia $2 \mathrm{~kg}$ $\mathrm{m}^2$ about its vertical axis, rotates at the rate of $60 \mathrm{rpm}$ about the axis. The torque which can stop the wheel's rotation in one minute would be:

  • A
    $\frac{2 \pi}{15} \mathrm{~N}-\mathrm{m}$
  • B
    $\frac{\pi}{12} \mathrm{~N}-\mathrm{m}$
  • Correct answer
    C
    $\frac{\pi 5}{15} \mathrm{~N}-\mathrm{m}$
  • D
    $\frac{\pi}{18} \mathrm{~N}-\mathrm{m}$

Solution

Given, $\mathrm{I}=2 \mathrm{~kg}-m^2$, $\omega_0=\frac{60}{60} \times 2 \pi \mathrm{rad} / \mathrm{s}$ $\omega_0$ and $t=60 \mathrm{~s}$ The torque required to stop the wheel's rotation is $\begin{aligned} \tau & =\mathrm{I} \propto l\left(\frac{\omega_0-\omega}{t}\right) \\ \tau & =\frac{2 \times 2 \pi \times 60}{60 \times 60} \\ & =\frac{\pi}{15} \mathrm{~N}-\mathrm{m} \end{aligned}$

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

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