The density of the core of planet is `rho_(1)` and that of the outer shell is `rho_(2)`. The radius of the core that of the planet are R and 2R respectively. Gravitastional intensity at the surface of the planet is same as at a depth R. Find the ratio `(rho_(1))/(rho_(2))` , assuming them to be uniform independently.

Answer

`7//3`

Explanation

`(GM_("core"))/(R^(2))=(GM_("Total"))/(4R^(2)), (G(4)/(3)piR^(3)rho)/(R^(2))=(G(4)/(3)piR^(3)[rho_(1)+7rho_(2)])/(4R^(2))`
`4rho_(1)=rho_(1)+7rho_(2) rArr (rho_(1))/(rho_(2))=(7)/(3)`