Consider a sphere of mass M and radius R. Calculate the gravitational potential energy of the...
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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 p(r) = pc(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. 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 p(r) = pc(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.
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