a) A planet of radius R has a core of radius R/2 which has a uniform density ρc. The mantle also has a uniform density ρm and the two densities are related by ρc = yρm
Determine y if C/MR^2 = 1/3.
b) Assume the average density of the entire Earth ρE = 5515 kg/m3 . Using the result you found for y, derive the average densities of the core and mantle, ρc and ρm, respectively. For comparison, the volume-averaged densities on Earth are ρm = 4480 kg/m3 and ρc = 10640 kg/m3 . Comment on what the main reason is for why the approximate values are different from the observed average densities.