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.

The density of the core of planet is rho_(1) and that of the outer she

1.	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» SOLUTION :`(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)`