Question

From a circular disc of radius R and mass 9M, a small disc of radius $\frac{R}{3}$ is removed. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is:

• A. $4M{R}^2$
• B. $\frac{40}{9}M{R}^2$
• C. $10M{R}^2$
• D. $\frac{37}{9}M{R}^2$

Answer 1

The correct option is A $4M{R}^2$

$\frac{m_1}{A_1}=\frac{m_2}{A_2}\frac{9M}{\pi R^2}={\frac{m_2}{\pi \left(\frac{R}{3}\right)}}^2.m_2=M{I}_{rem}=I_{whole}-I_{removed}=\frac{1}{2}9M{R}^2-[\frac{1}{2}M{\left(\frac{R}{3}\right)}^2+M{\left(\frac{2R}{3}\right)}^2]I_{rem}=4M{R}^2$