Question

A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with $10.0cm$ of water in one arm and $12.5cm$ of spirit in the other. The specific gravity of spirit would be.

• A. 0.70
• B. 0.80
• C. 0.90
• D. 0.60

Answer 1

Answer: (B)

Height of water column $h_1=10.0cm$
Density of water $\left({\rho }_1\right)=1g/c{m}^3$
Height of spirit column $\left(h_2\right)=12.5cm$
Density of spirit $\left({\rho }_2\right)=?$
The mercury column in both arms of the $U$-tube are at same level,
therefore pressure in both arms will be same.
$\therefore$ Pressure exerted by water column $=$ Pressure exerted by sprit column
$\therefore p_1=p_2$
$h_1{\rho }_{1}g=h_2{\rho }_{2}g$
or ${\rho }_2=\frac{h_1{\rho }_1}{h_2}=\frac{10\times 1}{12.5}=0.80g/c{m}^3$
Specific gravity of spirit $=\frac{\text{ Density of spirit }}{\text{ Density of water }}$
$=\frac{0.80}{1}=0.80$