A spherical body of radius  R consists of a fluid of constant density and is in equilibrium under its own gravity.  If  Pr is the pressure at  rr

The acceleration due to gravity at x from center =g=Gmx2=Gρ43πx3x2=43Gρπx On the element dm of thickness dx, the inward gravitational force is balanced by the outward pressure. −dP(A)=(dm)g⇒−dPA=(ρAdx)43GρπxIntegrating,⇒P=kR2−r2 Note: Assume pressure P=0 at r=RNow, check all options