MHT CET · Physics · Rotational Motion
A solid sphere is in purely rotational motion about its diameter. The ratio of its angular momentum and kinetic energy is \(\frac{\pi}{22}\). Find angular velocity of the sphere. ( \(\pi=22 / 7\) )
- A \(10 \mathrm{rad} / \mathrm{s}\)
- B \(7 \mathrm{rad} / \mathrm{s}\)
- C \(14 \mathrm{rad} / \mathrm{s}\)
- D \(21 \mathrm{rad} / \mathrm{s}\)
Answer & Solution
Correct Answer
(C) \(14 \mathrm{rad} / \mathrm{s}\)
Step-by-step Solution
Detailed explanation
\( \frac{L}{K} = \frac{I\omega}{\frac{1}{2}I\omega^2} = \frac{2}{\omega} \) \( \frac{2}{\omega} = \frac{\pi}{22} \)
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