Question

The ratio of radius of gyration of uniform hollow sphere and uniform solid sphere about its diameter is ______. (Both having same radius)

(1) \(\sqrt{\frac 43}\)

(2) \(\sqrt{\frac 53}\)

(3) \(\sqrt{\frac 32}\)

(4) \(\sqrt{\frac 35}\)

Answer 1

Correct option is (2) \(\sqrt{\frac 53}\)

For hollow sphere,

\(l_1 = \frac 23 mR^2 = mk_1^2, k_1 = \sqrt \frac 23 R\)

For solid sphere,

\(l_2 = \frac 25 mR^2 = mk_1^2, k_1 = \sqrt \frac 25 R\)

\(\frac {k_1}{k_2} = \sqrt {\frac 23 \times \frac 52 } = \sqrt \frac 53\)