Question

The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axis is :

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

Answer 1

The correct option is B $1:\sqrt{2}$

Radius of navigation is given by
$K=\sqrt{\frac{l}{m}}$
For given problem
$\frac{K_{disc}}{K_{ring}}=\sqrt{\frac{l_{disc}}{i_{ring}}}$
$\frac{K_{disc}}{K_{ring}}=\sqrt{\frac{\frac{1}{2}M{R}^2}{M{R}^2}}=1:\sqrt{2}$