Question

A soap film is formed in a circular frame. A loop of thread of length $2\pi r$ is lying on the film. Film inside the loop is broken then the tension in the thread will be
A. $2\pi rT$
B. $\pi rT$
C. $2rT$
D. $\pi {r^2}T$

Answer 1

Hint This is the question of the surface tension. Let F be the common magnitude of the forces exerted on each other by the two parts of the surface across a line of length l. We define the surface tension S of the liquid as:
$S = \dfrac{F}{L}$
The S.I. unit of surface tension is $N{m^{ - 1}}$

Complete Step by step solution

As we have seen in the question the film is formed in the circular frame.
And we all know that fluid has a tendency to decrease the surface area.
So to decrease the surface area we fluid will have tension on its surface so that the area could be contracted.
Let at any point on the surface of the ring there is tension called as $T$
Now we have a thread of length $2\pi r$. So to make a ring with thread of given length we will have same tension on each point of thread as like T
So total surface tension of the thread of given length will be:
Length of thread$ \times $tension on single point of thread
So total tension on the thread will be $2\pi rT$.

Therefore, option number A will be the correct answer.

Note
Surface is the property of the liquid in the earth. They have the contracting property means they have a tendency to decrease the surface area .Between the ring and the liquid a tension is found which is equal to the surface tension of the liquid.