Question

A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with $10.0\, cm$ of water in one arm and $12.5 \,cm$ 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 $h_{1}=10.0\, cm$
Density of water $\left(\rho_{1}\right)=1 g / cm ^{3}$
Height of spirit column $\left(h_{2}\right)=12.5\, cm$
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 $\rho_{2}=\frac{h_{1} \,\rho_{1}}{h_{2}}=\frac{10 \times 1}{12.5}=0.80 \,g / cm ^{3}$
Specific gravity of spirit $=\frac{\text { Density of spirit }}{\text { Density of water }}$
$=\frac{0.80}{1}=0.80$