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A thin and light thread of sufficient le...

A thin and light thread of sufficient length `L` is attached to a wire frame. The frame (along with the thread) is dipped into soap solution. When the frame is taken out of the solution, the thread takes the form of a semicircle with a soap film extending between the frame and the thread as shown in the figure (`a`). Now the thread is deformed into two semicircles by applying a force of `F` at the middle of the thread, as a result the film gets strectched as shown in the figure. (`b`). Calculate the surface tension of the soap solution.

A

`(piF)/(2L)`

B

`(piF)/(L)`

C

`(2piF)/(L)`

D

`(1)/(4)(piF)/(L)`

Text Solution

Verified by Experts

From FBD
`F+2T=2sigmax`, where `T=2(sigma(x)/(4))`
`rArr F=sigmax` and `2((pix)/(4))=L`
`rArrsigma=(piF)/(2L)`
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