Question

A soap bubble of diameter $10\text{mm}$ has an excess pressure of $50{\text{N/m}}^2$. Find the surface tension of soap solution.

• A. $0.31\text{N/m}$
• B. $0.063\text{N/m}$
• C. $0.063{\text{N/m}}^2$
• D. $0.031{\text{N/m}}^2$

Answer 1

The correct option is B $0.063\text{N/m}$

Given,
Diameter of soap bubble $\left(d\right)=10\text{mm}$
$\therefore$ Radius $\left(r\right)=\frac{d}{2}=5\times {10}^{-3}\text{m}$
Excess pressure, $\Delta P=50{\text{N/m}}^2$

From the definition, excess pressure of a soap bubble is given by
$\Delta P=P_i-P_0=\frac{4T}{r}$
From the data given in the question,
$50=\frac{4T}{5\times {10}^{-3}}$
$\Rightarrow T=\frac{50\times 5\times {10}^{-3}}{4}=0.0625\text{N/m}\approx 0.063\text{N/m}$
$=0.063\text{N/m}$
Thus, option (c) is the correct answer.