Question

A U-tube in which the cross-sectional area of the limb on the left is one-third that of the limb on the right contains mercury. The level of the mercury in the narrow limb extends to a distance of 30 cm from the upper end of the tube. To what height will the level of the mercury rise in the right limb if the left limb is filled to the top with water?  

Answer 1

Answer: A₂ ≅ 0.6cm.

Explanation:

When the water is poured in, the level of the mercury in the narrow limb is depressed by a height h₁, and in the wide limb it rises by a height h₂ = h₁/3. The height of the water is l + h₁ where l is the distance from the surface of the mercury to the top of the narrow limb before the water was added; the height of the equivalent weight of mercury is h₁ + h₂. The equation of equilibrium is