The normal density of gold is p and its bulk modulus is K The increase in density of a lump of gold when a pressure P applied uniformly on all side is

K=P(ΔV/V)  or  ΔVV=PK………..(1)Further.ρ=MV  and  ρ′=MV−ΔV∴ ρ′ρ=VV−ΔV=1{1−(ΔV/V)}=1−ΔVV−1=1+ΔVV………..(2)From eqs. (1) and (2), we getρ′ρ=1+PK  or  ρ′ρ−1=PKor ρ′−ρρ=ρK  or  ρ′−ρ=ρPK