First slide

Moment of inertia

Question

The moment of inertia of a solid sphere of mass M and radius R about a tangent to the sphere is

Moderate

A

$\frac{2}{5} {MR}^{2}$
B

$\frac{6}{5} {MR}^{2}$
C

$\frac{4}{5} {MR}^{2}$
D

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

Solution

Moment of inertia of the solid sphere of mass M and radius R about any diameter is
$I_{diameter} = \frac{2}{5} {MR}^{2}$
According to theorem of parallel axes
$I_{tangent} = I_{diameter} + {MR}^{2}$
$= \frac{2}{5} {MR}^{2} + {MR}^{2} = \frac{7}{5} {MR}^{2}$

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