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Moment of inertia of a thin spherical shell about a tangent is I. What will be the moment of inertia of a solid sphere of same mass and radius about a diameter?

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$\frac{2 I}{25}$

$\frac{I}{3}$

$\frac{6 I}{25}$

$\frac{3 I}{25}$

answer is C.

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Detailed Solution

$\begin{array}{l} I = \frac{2}{3} m R^{2} + m R^{2} = \frac{5}{3} m R^{2} \\ I^{1} = \frac{2}{5} m R^{2} = \frac{2}{5} \times (\frac{3}{5} I) = \frac{6}{25} I \end{array}$

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