Question

There is a horizontal film of soap solution. On it a thread is placed in the form of a loop. The film is punctured inside the loop 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. $\frac{\pi R^2}{T}$
• B. $\pi R^{2}T$
• C. $2\pi RT$
• D. $2RT$

Answer 1

Answer: (D)

$2RT$

Let the surface tension be F in thread($2T\Delta l$) for a small part $\Delta l$

$\Delta l=R\theta$

$2F\sin \frac{\theta }{2}=2T\Delta l=2TR\theta$

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