Question

Find density of ethyl alcohol. Using information given in the diagram below

• A. $0.83 \,gcm ^{-3}$
• B. $0.5 \,gcm ^{-3}$
• C. $1.83 \,gcm ^{-3}$
• D. $0.12\,gcm ^{-3}$

Answer 1

Answer: (A)

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,
$\rho_{2} =\frac{\rho_{1}}{1.2}=\frac{1000}{1.2}=833.3\, kg / m ^{3}$
$=0.83\, g\,cm ^{-3}$