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

For a thin spherical shell, outward pressure force is $-4\pi r^2(dP/dr)dr$ and inward weight is $GM(r)\rho (4\pi r^{2}dr)/r^2$. Balance gives $\boxed{dP/dr=-GM(r)\rho /r^2}$. This assumes approximately spherical, slowly evolving structure without important rotational or magnetic support.