Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is 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
$I_{disc}=\frac{1}{2}{M}_{disc}{R}^2=\frac{1}{2}\left(4M_{sector}\right)R^2$
Now, $I_{sector}=\frac{I_{disc}}{4}$
$\Rightarrow I_{sector}=\frac{1}{2}M{R}^2.$