Question

The radius of the Earth is 6.37×106 m. Assume a simple non-uniform model of its density, where the inner region has a density of 8.3×103 kg/m3, and the outer region has a density of 2.8×103 kg/m3. Given that the rotational inertia of the Earth is 8.40×1037 kg⋅m2, what is the radius of the inner region?