Question

What is the effective density $\rho$ of the mixture of water and milk when they are taken with same volumes, where ${\rho }_1$ and ${\rho }_2$ are the densities of water and milk respectively?

• A. $\rho =$ $\frac{1}{2}$(${\rho }_1$+${\rho }_2$)
• B. $\rho =$ $\frac{1}{2}$($2{\rho }_1$+$2{\rho }_2$)
• C. $\rho =$ (${\rho }_1$+${\rho }_2$)
• D. $\rho =$ $\frac{1}{4}$($2{\rho }_1$+$2{\rho }_2$)

Answer 1

Answer: (A), (D)

The correct options are
A $\rho =$ $\frac{1}{2}$(${\rho }_1$+${\rho }_2$)
D $\rho =$ $\frac{1}{4}$($2{\rho }_1$+$2{\rho }_2$)

Given, the volume of water and milk is same $v$ and assume that their masses are $m_1$ and $m_2$.
we know that,
$m=$$\rho$$v$
Then mass of water $m_1={\rho }_1$$v$
and mass of milk $m_2={\rho }_2$$v$

Total mass of water and milk is:
$m_1+m_2={\rho }_1$$v+$${\rho }_2$$v$
$m_1+m_2=$$v({\rho }_1+{\rho }_2)$

Total volume of water and milk $V=2v$
The effective density of the mixture is:
$\rho =$ $\frac{Totalmass}{Totalvolume}$
$\rho =$ $\frac{v\left({\rho }_1\right)\left({\rho }_2\right)}{2v}$
$\rho =$ $\frac{1}{2}$(${\rho }_1$+${\rho }_1$)