Question

The mass of a thin circular plate is $M$ and its radius is $R$. About an axis in the plane of plate at a perpendicular distance $\frac{R}{2}$ from centre of plate, its moment of inertia is:

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

Answer 1

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

Moment of Inertia of a plate about any axis perpendicular to its plane is $\frac{M{R}^2}{2}$

By perpendicular axis theorem, moment of Inertia about any diameter is $\frac{1}{2}\left(\frac{M{R}^2}{2}\right)=\frac{M{R}^2}{4}$.

By parallel axis, net moment of Inertia is $\frac{M{R}^2}{4}+\frac{M{R}^2}{4}=\frac{M{R}^2}{2}$