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. `3/7`
B. `9/4`
C. `7/3`
D. `3/8`

Answer

C

Explanation

Let `m_(1)` be the mass of the core and `m_(2)` be the mass of outer shell.
`g_(A)=g_(B)` (given) Then `(Gm_(1))/(R^(2))=(G(m_(1)+m_(2)))/((2R)^(2))`
`:. 4m_(1)=(m_(1)+m_(2))` or
`4{4/3piR^(2)rho_(1)}=4/3piR^(3)rho_(1)+{4/3pi(2R)^(3)-4/3piR^(3}rho_(2)`
`:. 4rho_(1)=rho_(1)+7rho_(2)rArr (rho_(1))/(rho_(2))=7/3`