Question

Equal masses of water and a liquid a relative density $2$ are mixed together, then the mixture has a density (in $gc{m}^{-3}$) of

• A. $2/3$
• B. $4/3$
• C. $3/2$
• D. $3$

Answer 1

The correct option is B $4/3$

Let the mass of liquid and water used to form the mixture be $m$ each.

Density of water be $\rho$.

Give, the relative density of liquid $RD=\frac{{\rho }_l}{{\rho }_w}=2$

Thus, the density of liquid is ${\rho }_l=2\rho$

Volume of water used is $V_w=m/\rho$

Volume of the liquid used is $V_l=m/\left(2\rho \right)$

Total mass $=m+m=2m$ and total volume $=V_1+V_2=3m/\left(2\rho \right)$

Density of the mixture is ${\rho }_m=2m/\left(3m/\right(2\rho \left)\right)=4\rho /3$

As density of water is $\rho =1{\text{g cm}}^{-3}$, we have density of the mixture as $4/3{\text{g cm}}^{-3}$