The ratio of radius of gyration of a solid sphere of mass M and radius R about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is :

Question

Aicharya · Accepted Answer

Radius of gyration of solid sphere about its own axis is given by,

$k_{s o l i d} = \sqrt{\frac{I}{M}} = \sqrt{\frac{\frac{2 M R^{2}}{5}}{M}} = \sqrt{\frac{2}{5}} R$

Similarly,

$k_{h o l l o w} = \sqrt{\frac{I}{M}} = \sqrt{\frac{\frac{2 M R^{2}}{3}}{M}} = \sqrt{\frac{2}{3}} R$

Therefore, required ratio would be

$\frac{k_{s o l i d}}{k_{h o l l o w}} = \sqrt{\frac{3}{5}}$ .

Note: This option was not present in the original paper.

The ratio of radius of gyration of a solid sphere of mass M and radius R about its own axis to the radius of…

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