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A U-tube of uniform cross-sectional area A is given a horizontal acceleration 'a' along the line joining its two vertical limbs, which are separated by a distance d. Find the difference in the liquid levels between the two limbs.

1. ad/g
2. g/ad
3. adg
4. ad + g

Correct answer: ad/g

Solution

Pressure difference between the two columns must supply the horizontal force to accelerate the liquid. For a horizontal separation d, the surface slope tan(theta) = a/g, so the height difference is d*tan(theta) = ad/g.

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