A solid sphere and a thin hollow spherical shell have the same mass and the same radius. The ratio of the radius of gyration of the solid sphere to that of the hollow spherical shell, about their respective diametric axes, is:

Step-by-step solution

Moment of inertia of a solid sphere about its diametric axis is I₁ = 2 5 MR^2 Radius of gyration of the solid sphere is K₁ = I₁ M = 2 5 R Moment of inertia of a thin hollow spherical shell about its diametric axis is I₂ = 2 3 MR^2 Radius of gyration of the hollow spherical shell is K₂ = I₂ M = 2 3 R The ratio of their radii of gyration is K₁ K₂ = 2 5 R 2 3 R = 3 5 The ratio is 3 : 5 Answer: 3 : 5