Question

There is a horizontal film of soap solution. A thread is placed on it, in the form of a loop. The film inside the loop is punctured and the thread becomes a circular loop of radius $R$. If the surface tension of the soap solution be $T$, then the tension in the thread will be,

• A. $4RT$
• B. $2\pi RT$
• C. $2RT$
• D. $4\pi RT$

Answer 1

The correct option is C $2RT$



Consider a very small portion of film, approximately similar to a straight part. Now, the forces on it are as shown below.


$F$ denotes the tension in the thread and $T$ denotes the surface tension.

$\therefore F=2T\times d$, is the force due to surface tension, since there are two free surfaces.

So, $2F$ sin $d\theta =2T\times [2\times R(d\theta \left)\right]$

we get $\sin \left(d\theta \right)\approx d\theta$, for small value of $d\theta$

The net force acting on the bubble is,
$2Fd\theta =4TRd\theta \Rightarrow F=2TR$

Hence, $\left(C\right)$ is the correct answer.