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An open U-tube of uniform cross-section holds water (density 10³ kg/m³), standing initially at 0.29 m from the bottom in each arm. Kerosene oil (immiscible with water, density 800 kg/m³) is poured into the left arm until the oil column is 0.1 m long. Find the ratio h1/h2 of the liquid heights in the two arms.

1. 15/14
2. 35/33
3. 7/6
4. 5/4

Correct answer: 35/33

Solution

Let the water surface in the left arm drop by x; it rises by x in the right arm. Balancing hydrostatic pressure of (0.1 m oil + remaining water) in the left arm against the taller water column in the right arm and using rho_oil/rho_water = 0.8 gives the offset. Working it out, the height ratio of the two liquid columns (oil+water left vs water right) is 35/33.

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