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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीTorques of equal magnitude \( \tau \) are applied to a hollow cylinder and a solid sphere, both having the same mass \( M \) and radius \( R \). Both rotate from rest about their standard axes of symmetry. The ratio of the angular speed acquired by the solid sphere to that acquired by the hollow cylinder after a given time \( t \) (\( \omega_{\text{sphere}} / \omega_{\text{cyl}} \)) is:
Correct answer · Option 1
\( 5/2 \)
Explanation
\( \omega = \alpha t = \frac{\tau}{I} t \). Here \( I_{\text{cyl}} = MR^2 \) and \( I_{\text{sphere}} = \frac{2}{5}MR^2 \). Thus, \( \frac{\omega_{\text{sphere}}}{\omega_{\text{cyl}}} = \frac{I_{\text{cyl}}}{I_{\text{sphere}}} = \frac{MR^2}{\frac{2}{5}MR^2} = \frac{5}{2} \).
