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

Answer 1

Answer: (D)

Moment of inertia of a uniform circular disc about an axis through its centre and perpendicular to its plane is $I_C=\frac{1}{2}M{R}^2$.
By the theorem of parallel axes,
$\therefore$ Moment of inertia of a uniform circular disc about an axis touching the disc at its diameter and normal to the disc is $I$.
$I=I_C+M{h}^2=\frac{1}{2}M{R}^2+M{R}^2=\frac{3}{2}M{R}^2.$