Question

When two metals with equal volumes are mixed together the density of the mixture is 4 kg/m3?

Answer 1

Answer:

We know that Mass/Volume = densityThat is, m/V = ρ

Let the mass, volume and density of the first metal and second metal be m1, V1, ρ1and 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