The density of the core a planet is `rho_(1)` and that of the outer shell is `rho_(2)`. The radii of the core and that of the planet are `R` and `2R` respectively. The acceleration due to gravity at the surface of the planet is same as at a depth `R`. Find the ratio of `(rho_(1))/(rho_(2))`

Options

A. `3//4`
B. `5//3`
C. `7//3`
D. `3//5`

Answer

C

Explanation

Let `m_(1)` is mass of core and `m_(2)` outer portion
`m_(1)=4/3piR^(3) rho_(1), m_(2)=4/3pi[(2R)^(3)-R^(3)] rho_(2)`
Given that `(Gm_(1))/(R^(2))=(G(m_(1)+m_(2)))/((2R)^(2)) implies (rho_(1))/(rho_(2))=7/3`