One end of a tube is connected to a soap bubble of radius r. The other end is connected to a manometer containing a liquid of density rho, and the height difference in manometer arms is h. Find the surface tension T of the soap solution.

T = 2*r*rho*h*g
T = r*h*rho*g/4
T = 2*pi*r*h*rho*g/2
T = r*h*rho*g/2

Correct answer: T = r*h*rho*g/4

Solution

A soap bubble has two surfaces, so excess pressure inside = 4T/r. The manometer reads this excess pressure as rho*g*h. So 4T/r = rho*g*h, giving T = r*rho*g*h/4.

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