Question

One quarter sector disc of radius 'R', has mass 'M'. Its moment of inertia about the axis shown in figure is.

• A. $\frac{1}{2}M{R}^2$
• B. $\frac{1}{4}M{R}^2$
• C. $\frac{1}{8}M{R}^2$
• D. $\sqrt{2}M{R}^2$

Answer 1

The correct option is A $\frac{1}{2}M{R}^2$

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, $I_{sector}=\frac{I_{disc}}{4}$
$\Rightarrow I_{sector}=\frac{1}{2}M{R}^2.$