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Question

A soap film has been developed over a wire loop. If surface tension of the soap solution is 0.015 N/m, find the tension in the thread loop of length 12.56 cm which is kept over the soap film, when the soap film inside it is pricked.


A
2×104 N
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B
4×104 N
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C
5×104 N
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D
3×104 N
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Solution

The correct option is D 3×104 N
Given, surface tension, S=0.015 N/m
Length of thread loop, d=12.56 cm
If the thread loop is kept over the soap film and soap film inside it is pricked, then due to surface tension, the loop takes the shape of a circle.
Let us suppose, tension in the thread is T and surface force of the soap film is F.
According to question:


Radius of thread loop,
r=d2π [circumference =2πr]
r=12.562×3.14
r=2 cm .........(1)
Now, l=2r=4 cm .......(2) [from (1)]
we know that, Surface tension S=Fl
F=Sl
=0.015×4×102 [from (2)]
F=6×104 N ..........(3)
From the figure, we can deduce that,
F=2T
T=F2=6×1042 [from (3)]
T=3×104 N
Hence, option (d) is the correct answer.

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