Manometer measures gauge pressure difference

Steps:

• In a U-tube manometer, one arm connects to the gas, the other to atmosphere at pressure p₀.
• Mercury level rises on the gas side by height h if gas pressure is lower than p₀.
• Pressure balance at the mercury interface: gas pressure + ρgh = p₀.
• Thus, gas pressure = p₀ - ρgh.

Why A is correct:

• Follows hydrostatic pressure formula ΔP = ρgh for the height difference in an open-end manometer.

Why the others are wrong:

• B: Applies when gas pressure exceeds p₀, raising mercury on the atmospheric side.
• C: Assumes no pressure difference, ignoring manometer reading h.
• D: Represents only gauge pressure ρgh, not absolute gas pressure.

Final answer: A