The height of mercury in a barometer at a place is 64 cm. What would be the height of water in a barometer at the same place? (Density of water = 1000 kg/m3; density of mercury = 13600 kg/m3)

8.7 m

Explanation:

The pressure due to the mercury of height h = 64 cm = 0.64 m is

P = ρ₁gh₁ where ρ₁ = density of mercury = 13600 kg/m³

P = 13600 kg/m³ × 9.8 m/s² × 0.64 m = 85299.2 Pa

Since this is the same pressure for the water,

P = ρ₂gh₂ where ρ₂ = density of water = 1000 kg/m³ and h₂ = height of water

h₂ = P/ρ₂g = 85299.2 Pa/(1000 kg/m³ × 9.8 m/s²) = 85299.2 Pa/9800 kg/m ²s² = 8.7 m