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Q.

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:

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a

2 : 5

b

5 : 3

c

5 : 2

d

$\sqrt{3}$ : $\sqrt{5}$

answer is B.

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Detailed Solution

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$\begin{array}{l} I_{ss} = \frac{2}{5} {MR}^{2} = {MK}_{ss}^{2} \Rightarrow K_{ss} = \sqrt{\frac{2}{5}} R \\ I_{HS} = \frac{2}{3} {MR}^{2} = {MK}_{HS}^{2} \Rightarrow K_{HS} = \sqrt{\frac{2}{3}} R \\ \frac{K_{ss}}{K_{HS}} = \sqrt{\frac{2}{5}} \times \sqrt{\frac{3}{2}} = \sqrt{\frac{3}{5}} \end{array}$

(No correct answer key, NTA has dropped this question)

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