Question

A U-tube is held in a vertical plane such that its two limbs are vertical with the middle portion horizontal as shown in the figure. Three liquids A, B and C are poured into it and in steady state their interfaces are as shown in the figure. Which of the following statements are correct?

This question has multiple correct options.
A. Height of the column of liquid A is greater than that of C.
B. Density of liquid A is less than that of liquid C.
C. Density of liquid B is maximum among three liquids.
D. Pressure at R is greater than that at S.

Answer 1

Hint: Greater the density of the liquid, lower it will sink in the mixture of fluids with different densities. A denser liquid will exert pressure on the less dense and push the less denser liquid upwards in the limbs of the U-tube.

Complete step-by-step answer:
We are given a U-tube in which three different liquids A, B and C have been poured. When they are allowed to settle down and achieve steady state we get the configuration as shown in the figure. We notice that all liquids have separated from each other. Liquid A floats in the left limb of the U-tube and its column extends from point P to Q. Like liquid A, liquid C has occupied the right column extending from point U to T. The third liquid, liquid B floats below the liquids at the bottom of the U-tube while other two liquids float above it. Its column extends from Q to R to S to T.
1. From the diagram, we can clearly note that the height of the column of liquid A is greater than the height of column of liquid C. Therefore, option A is correct.
2. A liquid which is denser than other liquids exerts pressure on less dense liquids. We notice that column of liquid A is pushed upwards by the weight of liquid C. Tis means that liquid C is denser than liquid A. Therefore, option B is also correct.
3. A liquid which has maximum density compared to other liquids tends to sink down. Therefore, liquid B has the highest density out of 3 liquids and option C is correct.
4. Option D is wrong because a liquid exerts the same pressure in all directions according to Pascal’s law so pressure at S and R should be equal.

Note: All the liquids have separated from each other because they do not mix or dissolve with each other. Such liquids are called immiscible liquids. The liquids which can readily mix or dissolve in one another are called miscible liquids.