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. $ MR^{2} $
• B. $ \frac{2}{5}MR^{2} $
• C. $ \frac{3}{2}MR^{2} $
• D. $ \frac{1}{2}MR^{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}MR^{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}+MR^{2} $
$ =\frac{1}{2}MR^{2}+MR^{2} $
$ =\frac{3}{2}MR^{2} $