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, (r1/r2), is then close to :

Engineering

Physics

Capillary and Pressure Difference due to Surface Tension

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, (r₁/r₂), is then close to :

3/5

4/5

2/5

2/3

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$h = \frac{2 S_{1} cosθ}{r_{1} ρ_{1} g}$

$h = \frac{2 S_{2} {cosθ}_{2}}{r_{2} ρ_{2} g}$

$\Rightarrow \frac{r_{1}}{r_{2}} = \frac{2}{5}$