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MHT CET · Physics · Rotational Motion

A bob of mass ' m ' is tied by a massless string whose other end is wound on a flywheel (disc) of radius ' \(R\) ' and mass ' \(m\) '. When released from the rest, the bob starts falling vertically downwards. If the bob has covered a vertical distance ' \(h\) ', then angular speed of wheel will be (There is no slipping between string and wheel, \(g\) - acceleration due to gravity)

  1. A \(\frac{2}{\mathrm{R}} \sqrt{\frac{\mathrm{gh}}{3}}\)
  2. B \(\frac{1}{\mathrm{R}} \sqrt{\frac{2 \mathrm{gh}}{3}}\)
  3. C \(R \sqrt{\frac{2 g h}{3}}\)
  4. D \(2 \mathrm{R} \sqrt{\frac{\mathrm{gh}}{3}}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{2}{\mathrm{R}} \sqrt{\frac{\mathrm{gh}}{3}}\)

Step-by-step Solution

Detailed explanation

\(mgh = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2\) \(mgh = \frac{1}{2}m(R\omega)^2 + \frac{1}{2}(\frac{1}{2}mR^2)\omega^2\)