A uniform capillary tube of inner radius r is dipped vertically into a beaker filled with water. The water…

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?
  1. For a given material of the capillary tube, h decreases with increase in r
  2. For a given material of the capillary tube, h is independent of σ
  3. If this experiment is performed in a lift going up with a constant acceleration, then h decreases
  4. h is proportional to contact angle θ

Solution

2σR=ρgh R→Radius of meniscus
h=2σRρg R=rcos⁡θ [r→radius of capillary; θ→ contact angle]
h=2σcos⁡θrρg
(A) For given material, θ=constant
h∝1r
(B) h depends on σ
(C) If lift is going up with constant acceleration,
geff=g+a
h=2σcos⁡θrρg+a It means h decreases
(D) h is proportional to cos⁡θ,Not θ

Asked in: JEE Advanced 2018 (Paper 1)

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