Question

A circular portion of radius R/2 is cut from a uniform circular disc of mass M and radius R
as shown in the figure. Find the moment of inertia of the remaining body about an axis
which is perpendicular to the plane of the disc and touches a point on the circumference of the disc as shown.

• A. $\frac{M{R}^2}{4}$
• B. $\frac{3M{R}^2}{4}$
• C. $\frac{11}{8}M{R}^2$
• D. $\frac{45}{32}M{R}^2$

Answer 1

The correct option is D $\frac{45}{32}M{R}^2$

$\frac{3M{R}^2}{2}=I+\frac{3m{R}^2}{8}$
Mass of the removed portion, $m=M{\left(\frac{\frac{R}{2}}{R}\right)}^2=\frac{M}{4}\frac{3M{R}^2}{2}=1+\frac{3M{R}^2}{32}\Rightarrow I=\frac{45M{R}^2}{32}$