Question

The moment of inertia of a thin uniform circular disc about one o f its diameters is $I$ . The moment of inertia about an axis perpendicular to the circular surface and passing through its center is

• A. $\sqrt{2}I$
• B. $2I$
• C. $\frac{I}{2}$
• D. $\frac{I}{\sqrt{2}}$

Answer 1

Answer: (B)

Let the moment of inertia about an axis perpendicular to the circular surface and passing through its center be $I_{c}$.
Moment of inertia about one of its diameter is $I$ i.e. $I _{ x }= I _{ y }= I$
Using perpendicular axis theorem: $I _{z}= I _{ x }+ I _{ y }$
$\therefore I _{ C }= I + I =2 I$