question_answer

There is rectangular wire frame having a thin film of soap solution. A massless thin wire of radius R and area of cross section A is placed on the surface of film and inside portion of the film is pricked. If surface tension of soap solution is S and Young's modulus of wire is Y then change in radius of the wire is:

A) \[\frac{S{{R}^{2}}}{AY}\]                  

B) \[\frac{2S{{R}^{2}}}{AY}\]

C) \[\frac{S{{R}^{2}}}{3AY}\]                

D) none of these

Correct Answer: B

Solution :

[B]

Consider an element of wire forming angle \[\theta \] at the center

\[2T\sin \frac{d\theta }{2}=2\times [S\times R\times d\theta ]\]

\[\therefore T=2SR\]

\[Y=\frac{Fl}{A\Delta l}\]

\[\frac{YA\times \Delta R}{R}=2SR\]

\[\Delta R=\frac{2S{{R}^{2}}}{YA}\]