Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is A. 2TR.

Consider the following diagram,

Suppose tension in the thread is F, then for small part Δl of thread,

$\Delta l=R\theta$

Balancing the forces in the vertical direction we have

$2Fsin\theta /2=2T\Delta l=2TR\theta$

$F=\frac{2TR\theta }{2sin\theta /2}$

$F=\frac{TR\theta }{\theta /2}=2TR$.