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Q.

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?

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a

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

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

d

ℎ is proportional to contact angle 𝜃

answer is A.

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Detailed Solution

2σR=ρgh here surface tension =σ ⇒h=2σRρg Using, R=rcosθ ⇒h=2σcosθrρg (A)For given material ,θ→ constant h∝1r(B) h depend on σ (C)If lift is going up with constant acceleration, geff=(g+a) h=2σcosθrρg+a ,It means h decreases.(D) h is proportional to cosθ not θ

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