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NEET 2004
Exam
NEET
Year
2004
Subject
Physics
Chapter
Rotational Motion

NEET 2004 · Physics · Rotational Motion

A wheel having moment of inertia 2 ~kg m^2 about its vertical axis,...

A wheel having moment of inertia 2 kg2 \mathrm{~kg} m2\mathrm{m}^2 about its vertical axis, rotates at the rate of 60rpm60 \mathrm{rpm} about the axis. The torque which can stop the wheel's rotation in one minute would be:

Options

  1. A2π15 N−m\frac{2 \pi}{15} \mathrm{~N}-\mathrm{m}
  2. Bπ12 N−m\frac{\pi}{12} \mathrm{~N}-\mathrm{m}
  3. Cπ515 N−m\frac{\pi 5}{15} \mathrm{~N}-\mathrm{m}
  4. Dπ18 N−m\frac{\pi}{18} \mathrm{~N}-\mathrm{m}

Correct answer

C. π515 N−m\frac{\pi 5}{15} \mathrm{~N}-\mathrm{m}

Step-by-step solution

Given, I=2 kg−m2\mathrm{I}=2 \mathrm{~kg}-m^2, ω0=6060×2πrad/sω0\omega_0=\frac{60}{60} \times 2 \pi \mathrm{rad} / \mathrm{s} \omega_0 and t=60 st=60 \mathrm{~s} The torque required to stop the wheel's rotation is τ=I∝l(ω0−ωt)τ=2×2π×6060×60=π15 N−m\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}
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