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Question:

The ratio of surface tensions of mercury and water is given to be 7.5 while the ratio of their densities is 13.6. Their contact angles, with glass, are close to 135° and 0°, respectively. It is observed that mercury gets depressed by an amount h in a capillary tube of radius r₁ while water rises by the same amount h in a capillary tube of radius r₂. The ratio (r₂/r₁) is then close to :

3/5

4/5

2/5

2/3

Solution:

Correct option is C. 2/5
h=2S₁cosθ₁/r₁ρ₁g
h=2S₂cosθ₂/r₂ρ₂g
⇒r₁/r₂=2/5