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

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?

TestHub · Accepted Answer

Pressure balance across the meniscus (R = radius of meniscus): $\frac{2 σ}{R} = ρ g h$

$R = \frac{r}{c o s θ} \Rightarrow h = \frac{2 σ c o s θ}{r ρ g}$

(A) For a given material θ is constant, so h ∝ 1/r: h decreases with increase in r.

Correct.

(B) h ∝ σ, so h is not independent of σ.

Wrong.

(C) In a lift going up with constant acceleration, g_eff = g + a: $h = \frac{2 σ c o s θ}{r ρ ( g + a )}$ so h decreases.

Correct.

(D) h is proportional to cos θ, not to θ.

Wrong.

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