Question

A wire forming a loop is dipped into soap solution and taken out so that a film of soap solution is formed. A loop of 6.28 cm long thread is gently put on the film and the film is pricked with a needle inside the loop. The thread loop takes the shape of a circle. Find the tension the the thread. Surface tension of soap solution = 0.030 N m⁻¹.

Answer 1

Given:
Surface tension of soap solution T = 0.030 N m⁻¹
Let the radius of the thread loop be r.

$$\begin{gathered} \Rightarrow 2\mathrm{\pi }r=6.28\mathrm{cm} \\ \Rightarrow r=\frac{6.28}{2\times 3.14}=1\mathrm{cm} \end{gathered}$$

The excess pressure inside the loop is expressed as follows:
$∆P=\frac{4T}{r}$

Tension in the thread:

$T\text{'}=∆P\times \left(\mathrm{area}\mathrm{of}\mathrm{loop}\right)$
$$\begin{gathered} \Rightarrow T\text{'}=\frac{4T}{r}\times \mathrm{\pi }{r}^2 \\ \Rightarrow T\text{'}=4\mathrm{\pi }Tr \\ =4\times 0.030\times 3.14\times {10}^{-2}\mathrm{N} \\ =3.8\times {10}^{-3}\mathrm{N} \end{gathered}$$