If two liquids of same masses but densities ρ1 and ρ2 respectively are mixed, then density of mixture is given by

The correct option is: ρ = 2ρ1ρ2/(ρ1 + ρ2)

To find the density of the mixture, we use the fundamental formula for density:

$\text{Density}=\frac{\text{Total Mass}}{\text{Total Volume}}$

Let the mass of each liquid be $m$ (since they are of equal mass). The total mass $M$ of the mixture is:

$M=m+m=2m$

Let the densities of the two liquids be ${\rho }_1$ and ${\rho }_2$ respectively. Since volume is given by mass divided by density, the individual volumes of the two liquids are:

$V_1=\frac{m}{{\rho }_1}$
and
$V_2=\frac{m}{{\rho }_2}$

The total volume $V$ of the mixture is the sum of these volumes:

$V=V_1+V_2=\frac{m}{{\rho }_1}+\frac{m}{{\rho }_2}$

Taking $m$ as a common factor and finding a common denominator, we get:

$V=m(\frac{1}{{\rho }_1}+\frac{1}{{\rho }_2})=m\left(\frac{{\rho }_1+{\rho }_2}{{\rho }_1{\rho }_2}\right)$

Substituting the expressions for total mass $M$ and total volume $V$ back into the density formula, the density $\rho$ of the mixture is:

$\rho =\frac{M}{V}=\frac{2m}{m\left(\frac{{\rho }_1+{\rho }_2}{{\rho }_1{\rho }_2}\right)}$

By canceling out $m$ from the numerator and denominator, we obtain:

$\rho =\frac{2}{\frac{{\rho }_1+{\rho }_2}{{\rho }_1{\rho }_2}}=\frac{2{\rho }_1{\rho }_2}{{\rho }_1+{\rho }_2}$

Therefore, the density of the mixture is given by the expression $\rho =\frac{2{\rho }_1{\rho }_2}{{\rho }_1+{\rho }_2}$.