There is a horizontal film of soap solution. On it a thread is placed in the form of a loop. The film is pierced inside the loop and the thread becomes a circular loop of radius R. If the surface tension of the loop be T, then what will be the tension in the thread
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Suppose tension in thread is F, then for small part $\Delta_A$ of thread
$\Delta l = R \theta$ and $2F \sin \theta / 2 = 2T \triangle l = 2TR \theta$
$\Rightarrow F = \frac{TR \theta}{\sin \theta / 2} = \frac{TR \theta}{\theta / 2} = 2TR (\sin \theta / 2 \approx \theta / 2)$
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