Capillary rise of mercury in a small diameter tube is proportional to (where, d = diameter of the tube, σ = surface tension of mercury)
A
d
B
$$\frac{1}{{\text{d}}}$$
C
$$\sigma $$
D
$$\frac{l}{\sigma }$$
Correct Answer: $$\sigma $$
The capillary rise of mercury in a small diameter tube is proportional to 1/d, whered is the diameter of the tube, and σ is the surface tension of mercury.Capillary rise occurs due to the balance between cohesive forces within the liquid and adhesive forces between the liquid and the tube wall. In a small diameter tube, the capillary rise is inversely proportional to the diameter of the tube.Mathematically, the capillary rise
h is given by the capillary rise equation:h = (2σ cosθ) / (ρgr)Where:
σ is the surface tension of the liquid (mercury).θ is the contact angle between the liquid and the tube wall (usually close to 0° for mercury in glass).ρ is the density of the liquid (mercury).g is the acceleration due to gravity.r is the radius of the tube (half of the diameter).Since the radius
r is directly proportional to 1/d, and the capillary rise is proportional to the radius r, the capillary rise is inversely proportional to the diameter d, which is represented by option B.
