Question

There is a horizontal film of soap solution. On it a thread is placed in the 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 loop be T, then what will be the tension in the thread

• A. $\pi R ^ { 2 } / T$
• B. $\pi R ^ { 2 } T$
• C. 2πRT
• D. 2RT

Answer 1

Answer: (D)

2RT

Answer 2

Suppose tension in thread is F, then for small part ∆l of thread

$2 F \sin \theta / 2 = 2 T \Delta l = 2 T R \theta$

$= \frac { T R \theta } { \sin \theta / 2 } = \frac { T R \theta } { \theta / 2 } = 2 T R ( \sin \theta / 2 \approx \theta / 2 )$