Question

The moment of inertia of a uniform circular disc of radius $R$ and mass $M$ about an axis touching the disc at its diameter and normal to the disc is

• A. $M{R}^2$
• B. $\frac{2}{5}M{R}^2$
• C. $\frac{3}{2}M{R}^2$
• D. $\frac{1}{2}M{R}^2$

Answer 1

Answer: (C)

The moment of inertia about an axis passing through centre of mass of disc and , perpendicular to its plane is
$I_{CM}=\frac{1}{2}M{R}^2$
where $M$ is the mass of disc and $R$ its radius.
According to theorem of parallel axis, moment of inertia of circular disc about an axis touching the disc at its diameter and normal to the disc is
$I=I_{CM}+M{R}^2$
$=\frac{1}{2}M{R}^2+M{R}^2$
$=\frac{3}{2}M{R}^2$