Two solid spheres of different materials have the same moments of inertia about their diameters. If `r_(1)` and `r_(2)` are their radii, ratio of their densities is

Options

A. `r_(1)^(3) : r_(2)^(3)`
B. `r_(2)^(3):r_(2)^(3)`
C. `r_(1)^(5):r_(2)^(5)`
D. `r_(2)^(5):r_(1)^(5)`

Answer

D

Explanation

`I_(1)=I_(2)`
`(2)/(5)M_(1)R_(1)^(2)=(2)/(5)M_(2)R_(2)^(2)`
`rho_(1)V_(1)R_(1)^(2)=rho_(2)V_(2)R_(2)^(2)`
`rho_(1)(4pi)/(3)R_(1)^(3)R_(1)^(2)=rho (4pi)/(3)R_(1)^(3)R_(2)^(3)`
`(rho_(1))/(rho_(2))=(R_(2)^(5))/(R_(1)^(5))`.