10.9 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. What is the specific gravity of spirit?

The given system of water, mercury, and methylated spirit is shown as follows:

Height of the spirit column,h1 = 12.5 cm = 0.125 m

Height of the water column, h2 = 10 cm = 0.1 m

P0 = Atmospheric pressure

ρ1 = Density of spirit

ρ2= Density of water

Pressure at point B = P0+h1ρ1g

Pressure at point D = P0+h2ρ2g

Pressure at points B and D are the same.

P0+h1ρ1g=P0+h2p2g
ρ1ρ2=h2h1
=1012.5=0.8

Therefore, the specific gravity of the spirit is 0.8.