Question

# There is a horizontal film of soap solution. A thread is placed on it, in the form of a loop. The film inside the loop is punctured and the thread becomes a circular loop of radius R. If the surface tension of the soap solution be T, then the tension in the thread will be,

A
4RT
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B
2πRT
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C
2RT
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D
4πRT
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Solution

## The correct option is C 2RT Consider a very small portion of film, approximately similar to a straight part. Now, the forces on it are as shown below. F denotes the tension in the thread and T denotes the surface tension. ∴F=2T×d, is the force due to surface tension, since there are two free surfaces. So, 2F sin dθ=2T×[2×R(dθ)] we get sin(dθ)≈dθ, for small value of dθ The net force acting on the bubble is, 2Fdθ=4TRdθ⇒ F=2TR Hence, (C) is the correct answer.

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