Question

Identify the correct order in which the ratio of radius of gyration to radius increases for the following bodies.
I) rolling solid sphere
II) rolling solid cylinder
III) rolling hollow cylinder
IV) rolling hollow sphere

• A. I, II, IV, III
• B. I, III, II, IV
• C. II, I, IV, III
• D. II, I, III, IV

Answer 1

The correct option is A I, II, IV, III

For solid sphere, the radius of gyration is $k=\sqrt{2R^2/5}=\sqrt{2/5}R$

For solid cylinder, the radius of gyration is $k=\sqrt{R^2/2}=\sqrt{1/2}R$

For hollow cylinder, the radius of gyration is $k=\sqrt{R^2}=R$

For hollow sphere, the radius of gyration is $k=\sqrt{2R^2/3}=\sqrt{2/3}R$

Arranging in increasing order, $I<II<IV<III$