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A soap bubble is blown at one end of a tube; the bubble has radius r. The excess pressure inside the bubble is measured by a manometer containing a liquid of density rho, in which the height difference of the two columns is h. Express the surface tension T of the soap solution.

1. T = 2 rho h g
2. T = rho h g / 4
3. T = 2 pi r h rho g / 2
4. T = r h rho g / 4

Correct answer: T = r h rho g / 4

Solution

For a soap bubble (two liquid-air interfaces) the excess pressure is delta_P = 4T/r. The manometer measures this excess pressure as the hydrostatic head rho*g*h. Setting 4T/r = rho*g*h gives T = r*rho*g*h/4. Note one of the original options (rhg/4) omits r and is dimensionally wrong; the correct relation includes r.

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