Question

The ratio of radius of gyration of a circular ring to that of a circular disc, each of same mass and same radius about their respective central axes is

• A. \(\sqrt{2} : \sqrt{3}\)
• B. \(1 : \sqrt{2}\)
• C. \(\sqrt{3} : \sqrt{2}\)
• D. \(\sqrt{2} : 1\)
• E. \(1 : 1\)

Hint:

Disc has smaller radius of gyration than ring.

Answer 1

The Correct Option is D

Concept: \[ I = Mk^2 \]

Step 1: For ring.
\[ I = MR^2 \Rightarrow k = R \]

Step 2: For disc.
\[ I = \frac{1}{2}MR^2 \Rightarrow k = \frac{R}{\sqrt{2}} \]

Step 3: Ratio.
\[ k_{ring} : k_{disc} = R : \frac{R}{\sqrt{2}} = \sqrt{2} : 1 \]