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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीA solid cylinder and a hollow cylinder have the same mass \( M \) and same outer radius \( R \). They rotate about their respective central longitudinal axes with angular speeds \( \omega_1 \) and \( \omega_2 \). If both cylinders possess the same rotational kinetic energy, the ratio of their angular speeds \( \omega_1 / \omega_2 \) is:
Correct answer · Option 2
\( \sqrt{2} \)
Explanation
Rotational kinetic energy \( K = \frac{1}{2}I\omega^2 \). For solid cylinder \( I_1 = \frac{1}{2}MR^2 \); for hollow cylinder \( I_2 = MR^2 \). Since \( K_1 = K_2 \), \( \frac{1}{2}(\frac{1}{2}MR^2)\omega_1^2 = \frac{1}{2}(MR^2)\omega_2^2 \implies \omega_1/\omega_2 = \sqrt{2} \).
