Question

When two liquids of the same volume but of different densities, ${\rho }_1$and ${\rho }_2$ are mixed together, then the density of the mixture is

• A. ${\rho }_1+p_2$
• B. $2{\rho }_1+2p_2$
• C. $\frac{{\rho }_1+p_2}{2}$
• D. $\frac{2{\rho }_1{p}_2}{{\rho }_1+p_2}$

Answer 1

The correct option is C

$\frac{{\rho }_1+p_2}{2}$

Explanation for correct option

(C)$\frac{{\rho }_1+p_2}{2}$

Density

• The density of a substance is its amount of mass per unit volume.

Calculation of density of mixture having the same volume

• Let the first liquid have mass $M_1$, density ${\rho }_1$ and Volume $V$.
• Let the second liquid have mass $M_2$, density ${\rho }_2$ and Volume $V$.

$$\begin{gathered} \text{Density of mixture}=\frac{M_1+M_2}{2V} \\ =\frac{p_{1}V+p_{2}V}{2V} \\ =\frac{p_1+p_2}{2} \end{gathered}$$

Explanation for incorrect option

The density of the mixture is $\frac{{\rho }_1+p_2}{2}$. So, the options (A), (B), and (D) are incorrect.

Hence, option (C) is correct. The density of the mixture is $\frac{{\rho }_1+p_2}{2}$.