Sydney Shaffer

2023-03-13

Density of a mixture is $\rho$, when fluids of densities ${\rho }_{1}$ 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 & Explanation

saltarenqa3

The right response is A $\rho =\frac{{\rho }_{1}+{\rho }_{2}}{2}$
As we know,

Let each liquid's volume be v. [equal proportion]
$⇒\rho =\frac{\left({\rho }_{1}×v+{\rho }_{2}×v\right)}{v}+v\phantom{\rule{0ex}{0ex}}⇒\rho =\frac{\left({\rho }_{1}+{\rho }_{2}\right)v}{2v}\phantom{\rule{0ex}{0ex}}⇒\rho =\left(\frac{{\rho }_{1}+{\rho }_{2}}{2}\right)$

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