From a complete ring of mass M and radius R, a $30^{0}$ sector is removed. The moment of inertia of the incomplete ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is

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$\frac{9}{12} {MR}^{2}$

$\frac{11.3}{12} {MR}^{2}$

${MR}^{2}$

$\frac{11}{12} {MR}^{2}$

answer is B.

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Detailed Solution

Mass of incomplete ring $= m - \frac{M}{2 π} \times \frac{π}{6} = M - \frac{M}{12} = \frac{11 M}{12}$ Moment of inertia of incomplete ring $= (\frac{11 M}{12}) R^{2} = \frac{11}{12} {MR}^{2}$

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