We have two spheres, one of which is hollow and the other solid. They have identical masses and moment of intertia about their respective diameters. The ratio of their radius is given by.

Options

A. `5 : 7`
B. `3 : 5`
C. `sqrt(3) : sqrt(5)`
D. `sqrt(3) : sqrt(7)`

Answer

C

Explanation

Let the radii of the thin spherical shell and the solid shpere are `R_(1)` and `R_(2)`, respectively.
Then the moment of inertia of the spherical shell about their diameters
`l = (2)/(3)MR_(1)^(2) " "…(1)`
and the moment of inertia of the solid sphere is given by
`l=(2)/(5)MR_(2)^(2) " "...(ii)`
From Eqs. (i) and (ii), we get
`(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_(2) = sqrt(3) : sqrt(5)`