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------------------------------------------------ Two capillary tubes P and Q are dipped vertically in water. If the height of the water level in capillary tube P is \(\frac{2}{3}\) of the height in capillary tube Q, what is the ratio of their diameters?

A. 4:3
B. 3:2
C. 2:3
D. 3:4

The ratio of the diameters of two capillary tubes P and Q when water level height in P is 2/3 of that in Q is 3:2. Therefore, the correct answer is (b) 3:2.

To answer the question about the ratio of the diameters of capillary tubes P and Q when the height of the water level in capillary tube P is 2/3 of the height in capillary tube Q, we apply the concept of capillary action. The height to which a liquid rises or falls in a capillary tube is inversely proportional to the tube's diameter, according to the formula
h = (constant)/d, where h is the height and d is the diameter.

In this case, if the height in tube P (hP) is 2/3 of the height in tube Q (hQ), then 2/3 = (constant)/dP / (constant)/dQ or dQ / dP = 2/3. By inverting both sides, we get dP/ dQ = 3/2, which means the diameter of tube P is 3/2 times the diameter of tube Q. Therefore, the correct answer is (b) 3:2.