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)

$\frac{3}{2}MR^2$

Answer 2

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
$I =I_{ CM }+M R^{2}$
$=\frac{1}{2} M R^{2}+M R^{2}$
$=\frac{3}{2} M R^{2}$