Question

The two limbs of a U-shaped capillary tube have radii of 1 and 2 mm, respectively. A small quantity of mercury is poured into the tube and one limb is connected to a vacuum pump. At what difference in the air pressure will the mercury levels in both limbs be the same? Which limb should be connected to the pump for this to occur? The surface tension of mercury is 480 dyn/cm. 

Answer 1

The pump should be connected to the narrow limb.

Explanation:

We denote the heights of the mercury columns before the pumping by h₁ and h₂. The mercury in the tube will be in equilibrium if the pressure on both sides of the cross-section AB (Fig.) from the mercury columns on both sides of the U-tube

are the same. The total pressure on each side of AB consists of the pressure dgh due to the weight of the mercury columns and the surface tension forces. The latter pressure is given by

Hence the condition of equilibrium may be expressed by the following relation:

The difference in the air pressure should compensate for the difference in heights of the mercury columns, i.e., it should be equal to (in millimetres of mercury)