Question:
when 2 metals with equal volume are mixed together the density of the mixture is 4kg/m3.when equal masses of two metals are mixed together , mixture density is 3kg/m3..calculate the densities of each metal...??
Answer:
We know that Mass/Volume = density That is, m/V = ρ
Let the mass, volume and density of the first metal and second metal be m1, V1, ρ1 and m2, V2 and ρ2.
Case 1: Volume of both metals are same and let it be equal to V
Hence, density = (m1 + m2) / 2V = (V ρ1 + V ρ2) / 2V = ρ1 + ρ2 / 2 = 4 Kg/m3 -----------Eqn (1)
Case 2: Mass of both metals are same and let it be equal to M
Hence, density = 2m / (v1 + v2) = 2m / ( m / ρ 1 + m / ρ 2) = 2m / m (ρ1 + ρ2) /ρ1ρ2 = 2ρ1ρ2 / ρ1+ ρ2 = 3 kg/m3 -----------Eqn (2)
Substitute (1) in (2) 3 = 2 ρ1ρ2 / (ρ1+ ρ2) gives ρ1ρ2 = 12 Hence, ρ1 = 12/ ρ2
Solving, we get ρ1 2 - 8 ρ2 + 12 = 0 ; ρ1 = 6 or 2 Hence, ρ2 = 2 or 6 kg/m3
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