A U - shaped tube has both ends open and is half full with water. Oil is carefully poured into the right side of the U - tube, so that it floats on top of the water and so that no oil gets past the middle (bottom) of the tube. The level of the top of the oil will be (density of oil

Engineering

Physics

Liquid Pressure

Surface Tension and Surface Energy

Forces and Types of Forces

Question

A U - shaped tube has both ends open and is half full with water. Oil is carefully poured into the right side of the U - tube, so that it floats on top of the water and so that no oil gets past the middle (bottom) of the tube. The level of the top of the oil will be (density of oil < density of water)

below the level of the top of the water in the left side of the U - tube.

above the level of the top of the water in the left side of the U - tube.

the same as the level of the top of the water in the left side of the U - tube.

the level of the top of the water on the right side will be the same as on the left side.

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

This involves fluid statics and pressure equilibrium. Since oil is less dense than water and doesn't mix, it floats. The key is that pressure at the bottom (midpoint) must be equal in both arms.

Let ρ_w and ρ_o be densities of water and oil (ρ_o < ρ_w). Let h_w be the water height above the bottom in the left arm. In the right arm, oil of height h_o pushes down on water, which is depressed by a distance d. The pressure balance at the bottom is:

$ρ_{w} g h_{w} = ρ_{o} g h_{o} + ρ_{w} g (h_{w} - d)$

Since ρ_o < ρ_w, the oil column h_o must be taller than the water displacement d to exert the same pressure. Therefore, the top of the oil is above the top of the water on the left.

Final Answer: above the level of the top of the water in the left side of the U - tube.