Question

The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is

• A. $ 2:3 $
• B. $ 2:1 $
• C. $ \sqrt{5}:\sqrt{6} $
• D. $ 1:\sqrt{2} $

Answer 1

Answer: (C)

Radius of gyration of disc about a tangential axis in the plane of disc is $\frac{\sqrt{5}}{2} R=K_{1}$, radius of gyration of circular ring of same radius about a tangential axis in the plane of circular ring is
$K_{2}=\sqrt{\frac{3}{2}} R $
$\therefore \frac{K_{1}}{K_{2}}=\frac{\sqrt{5}}{\sqrt{6}} $