A star can be considered as a shpherical ball of hot gas of radius R.Inside the star the density of the gas is `rho_r` at a radius r and mass of the gas within this region is `M_r`.The correct differential equation for variation of mass with respect to radius `((dM_r)/(dt))` is (refer to the adjacent figure)

In astronomy order of magnitude estimation plays an important role. The derivative `(dp)/(dr)` can be taken difference ratio `(DeltaP)/(Deltar)` . Consider the star has a radius R, pressure at its centre is `P_C` and pressure at outer layer is zero if the average mass is `M_0/2` and average radius `R_0/2` then the expression for `P_C` is

Answer

`P_C=(GM_0^2)/(R_0^4)xx(3/(2pi))`