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. What is the specific gravity of spirit?

Answer 1

given, Height of spirit column , $h_1$ = 12.5 cm
Height of water column $h_2$ = 10.0 cm

Let $P_0$ is the atmospheric pressure.
$\rho_1$ is the density of the spirit.
$\rho_2$= density of the water column.

Pressure due to spirit column at B =$P_0+\rho_1gh_1$
Pressure due to water column at D = $P_0+\rho_2gh_2$

Pressure is equal at the points having the same height from the ground i.e. at points B and D.
$\cancel{P_0}+\rho_1gh_1=\cancel{P_0}+\rho_2gh_2$

or, $\rho_1h_1=\rho_2h_2$

or, $\frac{\rho_1}{\rho_2}=\frac{h_2}{h_1}=\frac{10}{12.5}=0.8$

hence, specific gravity of spirit = 0.8