A liquid of density ρ fills a U-tube of horizontal separation ℓ. One arm is open to atmosphere at pressure P₀ and the other is connected to a gas at pressure Pₐ. The tube accelerates horizontally with acceleration a and the liquid levels remain equal. Find Pₐ. Image
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Question

A liquid of density ρ fills a U-tube of horizontal separation ℓ. One arm is open to atmosphere at pressure P₀ and the other is connected to a gas at pressure Pₐ. The tube accelerates horizontally with acceleration a and the liquid levels remain equal. Find Pₐ. Image

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G1 Physics · Accepted Answer

Step 1: Use hydrostatic equilibrium, P₂−P₁ = ρgΔh; in an accelerating fluid replace g by the effective acceleration where required. Step 2: Equate pressures at the same horizontal level or integrate pressure over the stated surface. Applying these relations to the given data gives A: P₀ − ρaℓ. Final answer: A.