Question

The density of core of a plenet is roh1 and that of the outer shell is roh2 the radii of the core and that of the plenet is R and 2R respectively . The acceleration due to gravity at the surface of the plenet is the same at the depth R. Find the ratio of Roh1/Roh2

Answer 1

mass of core=4/3×@×R^3 ×%2 ( %=rho)(@=pie)
=4/3×@×R^3 ×%2
mass of planet =mass of core +outer part
=4/3×@×R^3×%2+(4/3×2R^3 -
4/3×R^3)×@×%1
=4/3×@×%2×R^3+28/3(R^3)
×@×%1
acceleration at surface=acceleration at core
[G×(4/3×@×%2×R^3+ = [G×(4/3×@×%2×R^3)]
28/3×@×%1×R^3)]÷2(R^2) ÷(R^2)
[4/3×@×%2×(R^3)+28/3×@ =[8/3×@×%2×(R^3)]
×%1×(R^3)]
28/3×@×%1×(R^3) =4/3×@×%2×(R^3)
28/3×%1 =4/3×%1
28×%1 =4×%2
7×%1 =%2
{(%1) / (%2)}=1/7