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

Answer

B

Explanation

Let `R_(1) and R_(2)` be the raddi of the thin spherical shell and the solid sphere respectively. Then for the spherical shell
`I_(1)=(2)/(3)MR_(1)^(2)" [M.I. of a hollow sphere]"`
and for the solid sphere, `I_(2)=(2)/(5)MR_(2)^(2)`
It is given that, `I_(1)=I_(2)`
`therefore" "(2)/(3)MR_(1)^(2)=(2)/(5)MR_(2)^(2)`
`therefore" "(R_(1)^(2))/(R_(2)^(2))=((2)/(5))/((2)/(3))=(2)/(5)xx(3)/(2)=(3)/(5)`
`therefore" "(R_(1))/(R_(2))=sqrt((3)/(5))`