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

Step-by-step solution

Let the radii of the thin spherical and the solid sphere are R₁ and R₂ respectively. Then the moment of inertia of the spherical shell about their diameter I= 2 3 M R₁^2 ....(i) and the moment of inertia of the solid sphere is given by I= 2 5 M R₂^2 ....(ii) Given that the masses and moment of inertia for both the bodies are equal, then from Eqs. (i) and (ii) 2 3 M R₁^2= 2 5 M R₂^2 R₁^2 R₂^2 = 3 5 R R₂ = 3 5 R₁: R₂= 3 : 5