Question

Density of a mixture is $\rho$, when fluids of densities ${\rho }_1\text{and}{\rho }_2$ are mixed in the same proportion. Then:

• A. $\rho =\frac{{\rho }_1+{\rho }_2}{2}$
• B. $\rho =\frac{2{\rho }_1{\rho }_2}{{\rho }_1+{\rho }_2}$
• C. $\rho =\frac{{\rho }_1^2}{{\rho }_2}$
• D. $\rho =\frac{{\rho }_2^2}{{\rho }_1}$

Answer 1

The correct option is A $\rho =\frac{{\rho }_1+{\rho }_2}{2}$

As we know,
${\rho }_{\text{mixture}}=\frac{\text{Total mass}}{\text{Total volume}}$
[$\text{mass = volume}\times \text{density}$]
Let volume of each liquid be $v$. [equal proportion]

$\Rightarrow \rho =\frac{({\rho }_1\times v+{\rho }_2\times v)}{v+v}$
$\Rightarrow \rho =\frac{({\rho }_1+{\rho }_2)v}{2v}$
$\Rightarrow \rho =\left(\frac{{\rho }_1+{\rho }_2}{2}\right)$