One quarter sector is cut from a uniform disc of radius 'R'. This sector has ma

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One quarter sector is cut from a uniform disc of radius 'R'. This sector has mass 'M'. It is made to rotate about a line perpendicular to its plane and passing through the center of the original disc. Its moment of inertia about the axis of rotation is

One Quarter Sector Is Cut From A Uniform Disc Of Radius 'R'....

Options:

A . 12MR2

B . 14MR2

C . 18MR2

D . √2MR2

Answer: Option A
:
A
If we assume complete disc to be present, then it would have a mass 4 times the mass of the sector. Then, moment of inertia of the complete disc is

I_{d i s c} = \frac{1}{2} M_{d i s c} R^{2} = \frac{1}{2} (4 M_{s e c t o r}) R^{2}

Now,

I_{s e c t o r} = \frac{I_{d i s c}}{4}

\Rightarrow I_{s e c t o r} = \frac{1}{2} M R^{2} .

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