question_answer

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]

A) \[\pi {{R}^{2}}/T\]             

B) \[\pi {{R}^{2}}T\]

C) \[2\pi RT\]                              

D) \[2RT\]

Correct Answer: D

Solution :

Suppose tension in thread is F, then for small part \[\Delta l\] of thread               \[\Delta l=R\theta \] and \[2F\sin \theta /2=2T\Delta l=2TR\theta \]               \[\Rightarrow F=\frac{TR\theta }{\sin \theta /2}=\frac{TR\theta }{\theta /2}=2TR(\sin \theta /2\approx \theta /2)\]