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  4. What is the moment of inertia for a solid sphere w.r.t. a tangent touching to its surface?

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Q. What is the moment of inertia for a solid sphere w.r.t. a tangent touching to its surface?

AIIMSAIIMS 2011System of Particles and Rotational Motion

Solution:

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The moment of inertia for a solid sphere along its diameter is
$I_{\text {diameter }}=\frac{2}{5} M R^{2}$
Moment of inertia about a tangent touching to its surface,
$I_{\text {tangent }}=I_{\text {diameter }}+M R^{2}$
(using theorem of parallel axes)
$=\frac{2}{5} M R^{2}+M R^{2}$
$=\frac{7}{5} M R^{2}$