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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h is proportional to contact angle $θ$

For a given material of the capillary tube, h is independent of $σ$

If this experiment is performed in a lift going up with a constant acceleration, then h decreases.

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

answer is A, C.

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Detailed Solution

As we know $h = \frac{2 σcosθ}{{rρg}_{eff}}$
As 'r' increases, h decreases $h α \frac{1}{r}$
[ all other parameters remaining cons tan t]
Also $h ασ$
Further if lift is going up with an acceleration a ' then $g_{eff} = g + a . As g_{eff} increases,' h' decreses$
$Also h α \cos θ not hαθ$