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