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

Options

A. `5:7`
B. `3:5`
C. `sqrt3:sqrt5`
D. `sqrt3:sqrt7`

Answer

C

Explanation

Let the radii of the thin spherical shell and the solid sphere are `R_(1)andR_(2)` respectively. Then the moment of inertia of the spherical shell about their diameter
`I=(2)/(3)MR_(1)^(2)" "......(i)`
and the moment of inertia of the solid sphere is given by
`I=(2)/(5)MR_(2)^(2)" "......(ii)`
Given that the masses and moment of inertia for both the bodies are equal, then from Eqa. (i) and (ii)
`(2)/(3)MR_(1)^(2)=(2)/(5)MR_(2)^(2)implies(R_(1)^(2))/(R_(2)^(2))=(3)/(5)`
`implies(R_(1))/(R_(2))=sqrt((3)/(5))impliesR_(1):R_(2)=sqrt3:sqrt5`