Question

Two liquids of densities ${\rho }_1$ & ${\rho }_2$ having equal masses are mixed together. The density of mixture will be

• A. $\rho =\frac{m_1+m_2}{v_1+v_2}$
• B. $\rho =\frac{2{\rho }_1{\rho }_2}{{\rho }_1+{\rho }_2}$
• C. $\rho =\frac{{\rho }_1+{\rho }_2}{2{\rho }_1{\rho }_2}$
• D. $\rho =\frac{m_1+m_2}{\frac{m_1}{{\rho }_1}+\frac{m_2}{{\rho }_2}}$

Answer 1

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

Given,

For 1st liquid, mass $=m$ and density $={\rho }_1$

For 2nd liquid, mass $=m$ and density $={\rho }_2$

Total volume of the mixture $=m(\frac{1}{{\rho }_1}+\frac{1}{{\rho }_2})$

When both are mixed, the density of the mixture will be

$=\frac{2m}{m(\frac{1}{{\rho }_1}+\frac{1}{{\rho }_2})}=\frac{2{\rho }_1{\rho }_2}{({\rho }_1+{\rho }_2)}$