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

4

Explanation

`(GM)/(2R)^(2)=(GM^('))/(R^(2))`
`(M)/(4)=M`
`(4)/(3)piR^(3)p1+(4)/(3)pi(8R^(3)-R^(3))_(p2)=4((4)/(3)piR^(3)_p1)`
`p_(1)+7p_(2)=4p_(1)`
`(p1)/(p2)=(7)/(3)`