JEE Advanced | 2018Fluid MechanicsHard

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 isσ. 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?

Options

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

Solution

2σR=ρgh      [R → Radius of meniscus]h=2σRρg        R=cosθ    [r→  radius of capillary; q →contact angle]h=2σcosθrρg 
(A) For given material, q → constant
h∞1r
(C) If lift is going up with constant acceleration,
geff = (g + a)
h=2σcosθrρ(g+a)   It means h decreasesh is proportional to cosθ  Notθ 

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