The height of mercury column in a barometer in a Calcutta
laboratory was recorded to be 75 cm. Calculate this pressure in SI
and CGS units using the following data: Specific gravity of mercury
= 136, Density of water = 103 kg/m3, g = 9.8 m/s2 at Calcutta.
Pressure = hρg in usual symbols.
Given: h = 75 cm = 0.75 m
Specific gravity of mercury = 136
Density of water = 103 kg/m3
g = 9.8 m/s2
Specific gravity is defined as the ratio of density of a substance w.r.t density of any other substance. Primarily the specific gravity is measured w.r.t water
Density of mercury = 136 × 103 kg/m3 = 136 × 103 kg/m3 = ρ
Pressure exerted by a liquid is given by the relation
P = hρg
= 0.75 × 136 × 103 × 9.8
= 999600 Pa
= 10 × 105 N/m2 (approx.)
For CGS unit
CGS unit of Force ⇒ dyne
1 dyne = 10-5 N ⇒ 1 N = 105 dyne
1 m = 100 cm
10 × 105 N/m2 = 10 × 105 × 105 dyne / (100 cm)2
= 10 × 106 dyne /cm2 (CGS)