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 $
Show Answer
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) $
