Two spheres of equal masses, one of which is a thin spherical shell and the other solid sphere, have the same moment of inertia about their respective diameters. The ratio of their radii is

Step-by-step solution

Let the radii of the thin spherical shell and the solid sphere be R₁ and R₂ , respectively. Then, the moment of inertia of the shell about its diameter is given by, I _ shell = 2 3 MR ₁^2 ...(i) And the moment of inertia of the solid sphere is given by, I _ sphere = 2 5 MR ₂^2 ...(ii) Given that, the masses and moment of inertia for both the bodies are equal, then from equations (i) and (ii), array ll & 2 3 M R₁^2= 2 5 MR ₂^2 & R ₁^2 R ₂^2 = 3 5 & R ₁: R ₂= 3 : 5 array