A star of mass M and radius R is made up of gases. The average gravitational pressure compressing the star due to gravitational pull of the gases making up the star depends on R as

Step-by-step solution

Consider a spherical shell of radius r and radial thickness dr. P & P+d P are pressure at its inner and outer surface. Let g _ r = gravitational acceleration at distance r ( For equilibrium of this shell - array l (P+d P) (4 r² )+ (4 r² d r ) g_ r =(P) (4 r² ) = 3 M 4 R³ = . Density of sphere d P=- g_ r d r g_ r = 4 3 Gpr dP =- 4 3 G ² r d r array (-) ve sign indicates that pressure is decreasing with radius array l _ P ^ P₀ d P= _ r ^ R - 4 3 G ² r d r & P₀-P=- 4 3 G ² ( R² 2 - r² 2 ) & P=P₀+ 4 3 G ² ( R² 2 - r² 2