The two alloys consist of substances with densities equal to 3g / cm3 and 6g / cm3. In one alloy, the masses of the constituent substances are equal, in the other, the volumes. Find the ratio of the density of the alloys.
By definition, the density ρ = m / v, in the specific case we have:
ρ1 = m1 / v1; ρ2 = m2 / v2;
Then the density of the alloy with equal volumes ρv = ρ1V1 + ρ2V2 / (ρ1 + ρ2) = (ρ1 + ρ2) / 2
and when the masses are equal, ρm = (m1 + m2) / (m1 / ρ1 + m2ρ2) = 2ρ1ρ2 / (ρ1 + ρ2).
Hence we obtain that ρm / ρv = 2ρ1ρ2 / (ρ1 + ρ2) 🙁 ρ1 + ρ2) / 2 = 4ρ1ρ2 / (ρ1 + ρ2) ^ 2
4 * 3 * 6 / (3 + 6) ^ 2 = 72/9 ^ 2 = 72/81 = 8/9.
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