 Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2016/s29/3/b/solution

Build a solid uniform sphere from thin shells:

d C = (2/3) r^{2} (4 π ρ r^{2} d r)

C = 8 π ρ R^{5} /15

, while

M = 4 π ρ R^{3} /3

. Hence

C = 2 M R^{2} /5

. This is a spherical uniform-density model; planetary flattening modifies the exact relation.

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