A thin soapy film is stretched at the square frame with a length a=5.0cm. A slender flexible thread with negligible mass is fastened at two diagonal points of the frame, separating soapy film in two regions as shown at the picture below. The film on one side is pierced and the thread takes a circular shape. The length of the thread is $π a / 2$ and it is inextensible. Find the tension (in mN) in the thread if the surface tension of the soap film is 3mN/metre.

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Detailed Solution

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OA = OB = a = distance from circumference
Let us take a as radius of the arc then length should be $\frac{π}{2} a,$ which is satisfied. Hence, a is radius of quarter arc.
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$\Rightarrow 2 T \sin (\frac{d θ}{2}) = 2 S a d θ \Rightarrow T d θ = 2 S a d θ \Rightarrow T = 2 S a = 2 \times 3 \times 10^{- 3} \times 5 \times 10^{- 2} = 0.30 m N$