Question

A circular ring is rotating about an axis passing through its diameter. If its radius of gyration is $10cm$, diameter of the ring is:

• A. $10\sqrt{2}cm$
• B. $20cm$
• C. $20\sqrt{2}cm$
• D. $40cm$

Answer 1

Answer: (C)

$20\sqrt{2}cm$

By perpendicular axis theorem, moment of inertia about any two perpendicular axis is sum of moment of inertia's about any two areas in the plane
$I=I_1+I_2$
$2\left(I_1\right)=M{R}^2$ for a ring.
$I_1=\frac{M{R}^2}{2}=M{\left(\frac{R}{\sqrt{2}}\right)}^2$
with radius of gyration $\frac{R}{\sqrt{2}}=10$
$\Rightarrow R=10\sqrt{2}$
$\therefore diameter=20\sqrt{2}$