Question

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

• A. $0.83gc{m}^{-3}$
• B. $0.5gc{m}^{-3}$
• C. $1.83gc{m}^{-3}$
• D. $0.12gc{m}^{-3}$

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,
${\rho }_2=\frac{{\rho }_1}{1.2}=\frac{1000}{1.2}=833.3kg/m^3$
$=0.83gc{m}^{-3}$