Soap has surface tension σ. We make a plane soap film and on the soap film we placed a loop of rubber band of total length ℓ. The cross sectional area of the rubber band is S and its Young's modulus of elasticity is E. Now the film inside the loop is pierced. The rubber loop acquires a circular shape. Find the tension in the rubber loop.

Engineering

Physics

Surface Tension

Question

$\frac{Eσℓs}{πEs - σℓ}$

$\frac{Eσℓs}{πEs + σℓ}$

2σℓ

Es – ℓσ

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$2 σRθ = 2 T \frac{θ}{2}$

T = 2σR

$\frac{T}{s} = Y \times \frac{(2 πR - ℓ)}{ℓ} = \frac{Y}{ℓ} (\frac{2 πT}{2 σ} - ℓ)$

$Y = \frac{πTY}{σℓ} - \frac{T}{s}$

$\Rightarrow T = \frac{Yσℓs}{π {Ys}_{s} - σℓ}$

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