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

Question

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

Infinity Learn · Accepted Answer

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$$=$$Δ$$WaWa+$$ΔwwFor maximum percentage error,Δρρ×$$100=$$ΔWaWa×$$100+$$Δww×$$100$$ Given Δ$$Wa=0.1gf$$ and $$Wa=10.0gfw=10.0$$−$$5.0=5.0gf$$ Δ$$w=$$Δ$$Wa+$$Δ$$Ww=0.1+0.1=0.2gf$$ Δρρ×$$100=0.110.0$$×$$100+0.25.0$$×$$100$$                   $$=1+4=5$$

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 $\pm$ 0.1) gf and the weight in water is (5.0 $\pm$ 0.1) gf, then the maximum permissible percentage error in relative density is

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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

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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 $\pm$ 0.1) gf and the weight in water is (5.0 $\pm$ 0.1) gf, then the maximum permissible percentage error in relative density is