A planet is made of two materials of density `rho_(1)` and `rho_(2)` as shown in figure. The acceleration due to gravity at surface of planet is same as a depth `'R'`. The ratio of `(rho_(1))/(rho_(2))` is `x/3`. Find the value of `x`.

Answer

7

Explanation

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