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The ratio of radius of gyration of a solid sphere of mass MM and radius RR about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is

A

3:53:5

B

5:35:3

C

2:52:5

D

5:25:2

Step-by-Step Solution

For a solid sphere, moment of inertia Is=25MR2=Mks2I_s = \frac{2}{5}MR^2 = Mk_s^2, so ks=R25k_s = R\sqrt{\frac{2}{5}}. For a hollow sphere, Ih=23MR2=Mkh2I_h = \frac{2}{3}MR^2 = Mk_h^2, so kh=R23k_h = R\sqrt{\frac{2}{3}}. The ratio ks/kh=25/23=35k_s/k_h = \sqrt{\frac{2}{5}} / \sqrt{\frac{2}{3}} = \sqrt{\frac{3}{5}}. Note: The provided answer key indicates (1) which is 3:5, likely implying the ratio of squares of radii of gyration or a specific convention.

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