Hydrostatic pressure balance in U-tube Steps:

• Immiscible liquids P and Q form separate columns in each arm of the U-tube.
• In equilibrium, pressures at the bottom equalize: ρ_P g h_P = ρ_Q g h_Q.
• Diagram shows three equal distances x, with h_P = 2x (two segments) and h_Q = x (one segment).
• Ratio ρ_P / ρ_Q = h_Q / h_P = x / 2x = 1/2. Why A is correct:
• Pressure balance formula ρ_P h_P = ρ_Q h_Q directly yields ρ_P : ρ_Q = 1:2 for h_P = 2x and h_Q = x. Why the others are wrong:
• B: Requires h_Q / h_P = 2/3, but diagram gives 1/2.
• C: Requires h_Q / h_P = 3/2, reversing heights incorrectly.
• D: Requires h_Q / h_P = 2, swapping and doubling heights wrongly. Final answer: A