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Question

There is a horizontal film of soap solution on it a thread is placed in 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 soap solution is T, then the tension in the loop will be

A
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B
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C
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D
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Solution

The correct option is A. 2TR.

Consider the following diagram,


Suppose tension in the thread is F, then for small part Δl of thread,

Δl=Rθ

Balancing the forces in the vertical direction we have

2Fsinθ/2=2TΔl=2TRθ

F=2TRθ2sinθ/2

F=TRθθ/2=2TR.


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