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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीThe ratio of the radius of gyration of a thin uniform circular disc of radius \( R \) about an axis passing through its centre and perpendicular to its plane to that of a uniform solid sphere of radius \( R \) about its diameter is:
Correct answer · Option 3
\( \sqrt{\frac{5}{4}} \)
Explanation
For circular disc about perpendicular axis: \( k_{\text{disc}} = \sqrt{\frac{1}{2}R^2} = \frac{R}{\sqrt{2}} \). For solid sphere about diameter: \( k_{\text{sphere}} = \sqrt{\frac{2}{5}R^2} = R\sqrt{\frac{2}{5}} \). Thus \( k_{\text{disc}} / k_{\text{sphere}} = \frac{R/\sqrt{2}}{R\sqrt{2/5}} = \sqrt{\frac{5}{4}} \).
