Find an expression for equivalent relative density when (i) two substa

1.	Find an expression for equivalent relative density when (i) two substances of relative density ρ1 and ρ2 are mixed by equal mass, (ii) two substances of relative density ρ1 and ρ2 are mixed by equal volume.
Answer» (i) When two substances are mixed by equal masses, the volume of one substance + volume of second substance = volume of the mixed substance or, m/ρ₁ + m/ρ₂ = 2m/ρ or, 1/ρ₁ + 1/ρ₂ = 2/ρ or ρ = {2ρ₁ρ₂}/{(ρ₁ + ρ₂)} (ii) When two substances are mixed by equal volume, the Mass of one substances + Mass of second substance = Mass of mixed substance or, Vρ₁g + Vρ₂g = 2Vρg or, ρ₁ + ρ₂ = 2ρ or, ρ = ρ₁ + ρ₂ where ρ is the equivalent relative density.

Find an expression for equivalent relative density when (i) two substances of relative density ρ1 and ρ2 are mixed by equal mass, (ii) two substances of relative density ρ1 and ρ2 are mixed by equal volume.

Answer»

(i) When two substances are mixed by equal masses, the volume of one substance + volume of second substance = volume of the mixed substance

or, m/ρ₁ + m/ρ₂ = 2m/ρ

or, 1/ρ₁ + 1/ρ₂ = 2/ρ or ρ = {2ρ₁ρ₂}/{(ρ₁ + ρ₂)}

(ii) When two substances are mixed by equal volume, the

Mass of one substances + Mass of second substance

= Mass of mixed substance

or, Vρ₁g + Vρ₂g = 2Vρg

or, ρ₁ + ρ₂ = 2ρ

or, ρ = ρ₁ + ρ₂

where ρ is the equivalent relative density.