 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/s26/2/1/solution

- 4 π r^{2} (d P / d r) d r

and inward weight is

GM (r) ρ (4 π r^{2} d r) / r^{2}

. Balance gives

d P / d r = - GM (r) ρ / r^{2}

. This assumes approximately spherical, slowly evolving structure without important rotational or magnetic support.

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