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17. A uniform U-tube is partially filled with water. Oil, of density 0.75 g/cm3, is poured into theright arm until the water level in the left arm rises 3 cm. The length of the oil column is then:A. 2.25 cmB. 8 cmC. 6 cmD. 4 cmE. need to know the cross-sectional area of the U-tube

Question

  1. A uniform U-tube is partially filled with water. Oil, of density 0.75 g/cm3, is poured into theright arm until the water level in the left arm rises 3 cm. The length of the oil column is then:A. 2.25 cmB. 8 cmC. 6 cmD. 4 cmE. need to know the cross-sectional area of the U-tube
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Solution

The answer to this question can be found by understanding the principle of communicating vessels, which states that in a system of connected vessels, the liquid will balance out to the same level in all of the vessels regardless of the shape and volume of the vessels.

In this case, the U-tube is filled with two different liquids: water and oil. The oil is less dense than the water, so it will float on top of the water.

When the oil is poured into the right arm of the U-tube, it pushes down on the water, causing the water level in the left arm to rise. The question states that the water level in the left arm rises by 3 cm.

Since the oil is less dense than the water (0.75 g/cm3 compared to 1 g/cm3 for water), it will take a greater volume of oil to balance out the same volume of water.

The height of the oil column can be found by dividing the height of the water column by the relative density of the oil.

So, the height of the oil column is 3 cm / 0.75 = 4 cm.

Therefore, the correct answer is D. 4 cm.

This problem has been solved

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