Question

A soap film has been developed over a wire loop. If surface tension of the soap solution is $0.015\text{N/m}$, find the tension in the thread loop of length $12.56\text{cm}$ which is kept over the soap film, when the soap film inside it is pricked.

• A. $2\times {10}^{-4}\text{N}$
• B. $4\times {10}^{-4}\text{N}$
• C. $5\times {10}^{-4}\text{N}$
• D. $3\times {10}^{-4}\text{N}$

Answer 1

The correct option is D $3\times {10}^{-4}\text{N}$

Given, surface tension, $S=0.015\text{N/m}$
Length of thread loop, $d=12.56\text{cm}$
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,
$r=\frac{d}{2\pi }$ [circumference $=2\pi r$]
$\Rightarrow r=\frac{12.56}{2\times 3.14}$
$\Rightarrow r=2\text{cm}.........\left(1\right)$
Now, $l=2r=4\text{cm}.......\left(2\right)$ [from (1)]
we know that, Surface tension $S=\frac{F}{l}$
$\Rightarrow F=Sl$
$=0.015\times 4\times {10}^{-2}$ [from (2)]
$\Rightarrow F=6\times {10}^{-4}\text{N}..........\left(3\right)$
From the figure, we can deduce that,
$F=2T$
$\Rightarrow T=\frac{F}{2}=\frac{6\times {10}^{-4}}{2}$ [from (3)]
$\Rightarrow T=3\times {10}^{-4}\text{N}$
Hence, option (d) is the correct answer.