Thank you for reporting, we will resolve it shortly
Q.
Find density of ethyl alcohol. Using information given in the diagram below
Mechanical Properties of Fluids
Solution:
Pressure at left arm of U-tube,
$p_{1}=p_{0}+\rho_{1} g h_{1}$
$=p_{0}+\rho_{1} 10\left(10 \times 10^{-2}\right)$
or $p_{1}=p_{0}+\rho_{1}$
Pressure at right arm of U-tube,
$p_{2}=p_{0}+\rho_{2} g h_{2}$
$=p_{0}+\rho_{2} 10\left(12 \times 10^{-2}\right)$
or $p_{2}=p_{0}+1.2 \rho_{2}$
The mercury column in both arms of U-tube are at same level, therefore pressure in both arms will be same.
i.e. $ p_{1}=p_{2}$
$ \Rightarrow p_{0}+\rho_{1}=p_{0}+1.2 \rho_{2}$
$\therefore$ Density of ethyl alcohol,
$\rho_{2} =\frac{\rho_{1}}{1.2}=\frac{1000}{1.2}=833.3\, kg / m ^{3}$
$=0.83\, g\,cm ^{-3}$
