Question

A loop of 6.28 cm long thread is put gently on a soap film it a wire loop. The film is pricked with a needle inside the soap film enclosed by the thread. If the surface tension of soap solution is 0.030 N/m, then the tension in the thread is:

• A. $1\times {10}^{-4}N/m$
• B. $2\times {10}^{-4}N/m$
• C. $3\times {10}^{-4}N/m$
• D. $4\times {10}^{-4}N/m$

Answer 1

The correct option is C $3\times {10}^{-4}N/m$

When the soap film enclosed by the thread is picked, the thread would take up a circular shape. Consider a small element of the thread. While horizontal components of tension get balanced, the vertical components get added up.
Or $2Tsin\theta =\sigma \Delta l$
Or $2T\theta =\sigma (2\theta \times r)$
Or $T=\sigma r=\sigma \times \frac{2\pi r}{2\pi }=0.030\times \frac{6.28\times {10}^{-2}}{2\pi }N$
$=3\times {10}^{-4}N$