The relative density of a material is found by weighing the body first in air and then in water. If the weight in air is (10.0 ± 0.1) gf and the weight in water is (5.0 ± 0.1) gf, then the maximum permissible percentage error in relative density is

Relative density =WaWa−Ww,ρ=Wawwhere ρ is relative density, Wa is weight in air, and w is loss in weight.Δρρ=ΔWaWa−Δww For maximum error, Δρρ=ΔWaWa+ΔwwFor maximum percentage error,Δρρ×100=ΔWaWa×100+Δww×100 Given ΔWa=0.1gf and Wa=10.0gfw=10.0−5.0=5.0gf Δw=ΔWa+ΔWw=0.1+0.1=0.2gf Δρρ×100=0.110.0×100+0.25.0×100                   =1+4=5