An elliptically shaped ring of dimensions shown in figure just touches, the horizontal surface of a liquid of surface tension S. The force required to pull the ring away from the liquid surface is

Impurities: The surface tension decreases with the addition of impurities.
Surfactants: Adding surfactants in liquids lowers the tension of water making it interrupt aside or get susceptible.
Temperature: The surface tension of a liquid reduces as the temperature rises.

Internal mean radius $ {{r}_{1}}\sqrt{{{a}_{1}}{{b}_{1}}} $ Internal circumference of the ring $ =2\pi {{r}_{1}}=2\pi \sqrt{{{a}_{1}}{{b}_{1}}} $ External mean radius $ {{r}_{2}}=\sqrt{{{a}_{2}}{{b}_{2}}} $ External circumference of the ring $ =2\pi {{r}_{2}}=2\pi \sqrt{{{a}_{2}}{{b}_{2}}} $ Thus, force required $ F=2\pi \sqrt{{{a}_{1}}{{b}_{1}}S}+2\pi \sqrt{{{a}_{2}}{{b}_{2}}}\,S $ $ =2\pi (\sqrt{{{a}_{1}}{{b}_{1}}}+\sqrt{{{a}_{2}}{{b}_{2}}})S $

$ 2\pi (\sqrt{{{a}_{1}}{{b}_{1}}}+\sqrt{{{a}_{2}}{{b}_{2}}})S $

$ \pi ({{a}_{1}}+{{b}_{1}}+{{a}_{2}}+{{b}_{2}})S $

$ \pi \left( \frac{{{a}_{1}}+{{a}_{2}}}{2}+\frac{{{b}_{1}}+{{b}_{2}}}{2} \right)S $

$ \sqrt{2\pi }(\sqrt{{{a}_{1}}{{b}_{1}}}+\sqrt{{{a}_{2}}{{b}_{2}}})S $