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

Since the mercury column in the two arms is in the level, therefore,

Pressure of spirit = Pressure of water

⇒ ρ_sgh_s = ρ_wgh_w

⇒ ρ_s/ρ_w = h_w/h_s

But, ρ_s = density of spirit

ρ_w = density of water

h_s = height of spirit

= 12.5 cm = 12.5 x 10^-2 m

and h_w = height of water = 10 cm = 10 x 10^-2 m

From the relation

ρs/ρw = h_w/h_s = {10 x 10^-2}/{12.5 x 10^-2} = 0.8

i.e., sp gravity of spirit = ρ_s/ρ_w = 0.8