Properties Of Solids And Liquids Question 203

Question: 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[RPET 1996]

Options:

A) $ \pi R^{2}/T $

B) $ \pi R^{2}T $

C) $ 2\pi RT $

D) $ 2RT $

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Answer:

Correct Answer: D

Solution:

Suppose tension in thread is F, then for small part $ \Delta l $ of thread $ \Delta l=R\theta $

and $ 2F\sin \theta /2=2T\Delta 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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