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 $\sigma$. The angle of contact between water and the wall of the capillary tube is $\theta$. Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

(A) For a given material of the capillary tube, $h$ decreases with increase in $r$; (C) If this experiment is performed in a lift going up with a constant acceleration, then $h$ decreases

(B) For a given material of the capillary tube, $h$ is independent of $\sigma$

(D) $h$ is proportional to contact angle $\theta$

JEE Advanced · 2018 · 20 May 2018 · Paper 1 · Fluid Mechanics

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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?

(A)For a given material of the capillary tube, $h$ decreases with increase in $r$ ✓ Correct
(B)For a given material of the capillary tube, $h$ is independent of $σ$
(C)If this experiment is performed in a lift going up with a constant acceleration, then $h$ decreases✓ Correct
(D) $h$ is proportional to contact angle $θ$

Answer: (A), (C)

Solution

The capillary rise formula is

h = \frac{2 σ c o s θ}{ρ g r}

. From this: (A) When

r

increases,

h

decreases — correct. (B)

h

depends on

σ

— incorrect. (C) In a lift accelerating upward, effective

g

becomes

g + a

, so

h

decreases — correct. (D)

h

is proportional to

cos θ

, not

θ

— incorrect.

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JEE Advanced · 2018 · 20 May 2018 · Paper 1 · Fluid Mechanics

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