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

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 $I$.
$I=I_{C}+M h^{2}=\frac{1}{2} M R^{2}+M R^{2}=\frac{3}{2} M R^{2} .$