A non – homogeneous sphere of radius R has the following density variation ρ=ρ0  for  r≤R/3 ρ=ρ02  for R3< r≤3R4and ρ=ρ08  for 3R4 

For r=5R6,up toR3,ρ=ρ0, between R3and3R4, ρ=ρ02 and between 3R4 and 5R6, ρ=ρ08 ∴  The mass of the sphere of radius 5R/6 ism=43π(R3)3ρ0+[43π(3R4)3−43π(R3)3]ρ0/2 +[43π(5R6)3−43π(3R4)3]ρ0/8 =0.332 πR3ρ0 ∴  Gravitational field at a distance, r=5R6 isEg=Gm(5R/6)2 =G×0.332πR3ρ025R2×36 =0.48πGRρ0