Find the moment of inertia of a hemisphere of mass $M$ and radius $R$ shown in the figure, about an axis AA tangential to the hemisphere.

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$I = (\frac{9}{20}) m R^{2}$

$I = (\frac{13}{20}) m R^{2}$

$I = (\frac{7}{20}) m R^{2}$

$I = (\frac{3}{20}) m R^{2}$

answer is B.

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Detailed Solution

Moment of inertia about an axis through the flat face of hemisphere

$I_{G} = I_{B} - m {(\frac{3}{8} R)}^{2} = \frac{2}{5} m R^{2} - \frac{9}{64} m R^{2} = (\frac{83}{320}) m R^{2}$

Using parallel axis theorem, Moment of inertia about the axis AA',

$I = I_{G} + m {(\frac{5}{8} R)}^{2} \Leftrightarrow I = (\frac{13}{20}) m R^{2}$

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