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))`

Explanation

`(GM)/((2R)^(2))=(GM')/(R^(2))`
`(M)/(4)=M'`
`(4)/(3)piR^(3)rho_(1)+(4)/(3)pi(8R^(3)-R^(3))rho_(2)=4((4)/(3)piR^(3).rho_(1))`
`rho_(1)+7rho_(2)`
`(rho_(1))/(rho_(2))=(7)/(3)`