Question

A vertical uniform U-tube open at both ends contains mercury. Water is poured into one limb until the level of mercury is depressed 2 cm in that limb. What is the length of the water column when this happens?

(a) 1 cm
(b) 2 cm
(c) 3 cm
(d) 4 cm

Answer 1

The length of the water column that would depress the mercury by 2 cm in one limb of a U-tube is approximately 27.2 cm, calculated by using the ratio of the densities of mercury and water.

Step-by-step explanation:

To determine the length of the water column that depresses the mercury by 2 cm in one limb of a U-tube, we will use the principle that the pressure exerted by the height of the liquid in both limbs must be the same because the system is at equilibrium and the tube is open at both ends. Mercury is denser than water, specifically, mercury is about 13.6 times denser than water.

When water is added to one side of the U-tube, it depresses the mercury in that limb by 2 cm. Since the density of mercury is much greater, it requires a significantly larger column of water to depress the mercury by a certain height. Using the ratio of densities, we can calculate the height of the water column (hwater) needed to depress the mercury (hmercury) by:

hwater = hmercury × (Density of mercury / Density of water)

hwater = 2 cm × 13.6 ≈ 27.2 cm

Therefore, the correct answer is none of the options provided, as the water column would be approximately 27.2 cm tall.