A soap film has been developed over a wire loop. If surface tension of the soap solution is 0.015N/m, find the tension in the thread loop of length 12.56cm which is kept over the soap film, when the soap film inside it is pricked.
A
2×10−4N
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B
4×10−4N
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C
5×10−4N
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D
3×10−4N
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Solution
The correct option is D3×10−4N Given, surface tension, S=0.015N/m
Length of thread loop, d=12.56cm
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=2cm.........(1)
Now, l=2r=4cm.......(2) [from (1)]
we know that, Surface tension S=Fl ⇒F=Sl =0.015×4×10−2 [from (2)] ⇒F=6×10−4N..........(3)
From the figure, we can deduce that, F=2T ⇒T=F2=6×10−42 [from (3)] ⇒T=3×10−4N
Hence, option (d) is the correct answer.