Question

The ratio of radius of gyration of a solid sphere of mass M and radius R about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is :-

(1) 5 : 3

(2) 2 : 5

(3) 5 : 2

(4) 3 : 5

Answer 1

Correct option is (4) 3 : 5

Radius of gyration : K = \(\sqrt\frac{I}{m}\)

\(\frac{k_{solid \ sphere}}{k_{hollow\ sphere}}=\sqrt\frac{2mR^2/5m}{2mR^2/3m}\)

= \(\sqrt{3}:\sqrt{5}\)