A simple model of the Earth includes a dense spherical core of radius 4200 km and a less dense spherical shell of thickness 2180 km (Note: the radius of the Earth is 6380 km and the mass of the Earth is 5.98 E 24 kg.) If the density of the core in this model is 10.0 g/cc, find:
(a) the density of the shell;
(b) the moment of inertia of Earth;
(c) the rotational kinetic energy of Earth;
(d) and the number of years this energy could supply the human race with all our energy needs. (We currently use about 5.00 x 1020 Joules of energy, in all forms, per year.)