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Find the radius of gyration of a solid sphere of mass $M$ and radius $R$ about an axis $X X$ shown in figure.

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$\sqrt{\frac{7}{3}} R$

$\sqrt{\frac{7}{5}} R$

$\sqrt{\frac{3}{5}} R$

$\sqrt{\frac{1}{5}} R$

answer is B.

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Detailed Solution

From theorem of parallel axis,

$I_{X} = I_{COM} + {Mf}^{2} = \frac{2}{5} {MR}^{2} + {MR}^{2}$

$= \frac{7}{5} {MR}^{2}$

Radius of gyration.

$K = \sqrt{\frac{I}{M}} = \sqrt{\frac{7}{5}} R$

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