b) The observed axial moment of inertia of the Earth is 0.3307MERE2, Where ME = 5.972 x 1024 kg and RE = 6.371 x 106 m. Imagine the Earth as a sphere of uniform mantle density p M, (extending all the way to the center!) with a spherical core of uniform excess density Ape superimposed on the central part of the \"mantle\". In this case, the masses and moments of inertia of these spheres just add and the result is the same as a spherical shell of mantle surrounding a spherical core of density p c = p M + Ap . Take the radius of the c core as known, RC = 3.485 x 106 m. Solve for the densities of the mantle and of the core in this model, given the mass, moment of inertia, radius of the Earth, and radius of the core. c) You may notice that the resulting core density does not agree with the number given in Problem 1 of this problem set. Why not? (Hint: Both are \"right\" on their own terms. What assumptions did you make in each?)