Question

A liquid is used to make a mercury-type barometer. The barometer is intended for space-faring astronauts. At the surface of the Earth, the column of liquid rises to a height of 2185 mm, but on the surface of Planet X, where the acceleration due to gravity is ¼ its value on Earth, the column only rises to a level of 725 mm. Find the density of the liquid and the atmospheric pressure at the surface of Planet X

Answer 1

Density of liquid = 4730 kg/m³

Atmospheric pressure on planet X = 8401.7 N/m²

Step-by-step explanation:

Pressure, P = ρgh where ρ = density of liquid, g =9.8 m/s² and h = height of column at earth's surface = 2185 mm. Since P = atmospheric pressure, for mercury, P = ρ₁gh₁ where ρ₁ = 13.6 g/cm³ and h₁ = 760 mm

So, ρgh = ρ₁gh₁

ρ = ρ₁h₁/h = 13.6 g/cm³ × 760/2185 = 4.73 g/cm³ = 4730 kg/m³

The atmospheric pressure on planet X

P = ρg₁h₃ g₁ = g/4 and h₃ = 725 mm = 0.725 m

on planet X

P = ρg₁h₃ = (4730 kg/m³ × 9.8 m/s² × 0.725 m)/4 = 8401.7 N/m²