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Question:

A uniform capillary tube of inner radius r is dipped vertically into a beaker filled with water. The water rises to a height h in the capillary tube above the water surface in the beaker. The surface tension of water is σ. The angle of contact between water and the wall of the capillary tube is θ. Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

If this experiment is performed in a lift going up with a constant acceleration, then h decreases.

h is proportional to contact angle θ

For a given material of the capillary tube, h is independent of σ.

For a given material of the capillary tube, h decreases with increase in r

Solution:

2σR = ρgh [R → Radius of meniscus]
h = 2σR/ρg
R = rcosθ [r → radius of capillary; θ → contact angle]
h = 2σcosθ/ρgr
(A) For given material, θ → constant
h ∝ 1/r
(B) h depends on σ
(C) If lift is going up with constant acceleration, geff = (g+a)
h = 2σcosθ/ρ(g+a)r which means h decreases
(D) h is proportional to cosθ, NOT θ