Consider a sphere of mass M and radius R. Calculate the gravitational potential energy of the sphere assuming (a) a density which is independent of the distance from the centre, and (b) a density which increases towards the centre according to ρ(r)=(1-r / R) . In both cases, (a) and (b), write down the average internal pressure needed for hydrostatic equilibrium, and determine how the pressure within the sphere depends on the distance from the centre. | Numerade
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