Question

The moment of inertia of a thin uniform circular disc about one of the diameters is $l$. Its moment of inertia about an axis perpendicular to the plane of the disc and passing through its centre is

• A. $\left(\sqrt{2}\right)I$
• B. $2I$
• C. $I/2$
• D. $I/\sqrt{2}$

Answer 1

Answer: (B)

$2I$

Answer 2

Moment of inertia of thin uniform circular disc about one of its diameter is $I$ $\therefore I=\frac{MR^{2}}{4} \dots(i)$ where M is the mass and R is the radius of the disc. Moment of inertia of disc about an axis passing through the centre and perpendicular to the plane of the disc is $I$' $I' =\frac{MR^{2}}{2}=2 \left(\frac{MR^{2}}{4}\right)=2I$ [Using $(i)]$