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  4. The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is :

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Q. The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is :

NEETNEET 2022System of Particles and Rotational Motion

Solution:

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$k =\sqrt{\frac{ I }{ m }}$
$\Rightarrow \frac{ k _{1}}{ k _{2}}=\sqrt{\frac{ I _{1}}{ I _{2}}}$
$=\sqrt{\frac{ mR ^{2} / 2}{ mR ^{2} / 4}}=\sqrt{2}: 1$