Question

If the excess pressure inside a soap bubble of radius $1\text{cm}$ is balanced by an oil
($\rho =0.8{\text{g/cm}}^3)$ column of height $2\text{mm}$, then the surface tension of soap solution will be
[Take $g=10{\text{m/s}}^2$]

• A. $0.02\text{N/m}$
• B. $0.04\text{N/m}$
• C. $0.09\text{N/m}$
• D. $0.08\text{N/m}$

Answer 1

The correct option is B $0.04\text{N/m}$

Given,
Radius of soap bubble, $R=1\text{cm}={10}^{-2}\text{m}$
Density of oil, $\rho =0.8{\text{g/cm}}^3=800{\text{kg/m}}^3$
Height of oil column, $h=2\text{mm}=2\times {10}^{-3}\text{m}$
Let us suppose, surface tension of soap solution is $T$.
We know that, excess pressure inside soap bubble is given by
$\Delta P=\frac{4T}{R}$
$=\frac{4T}{{10}^{-2}}=400T$ .......(1)
Pressure due to height of oil column,
$P=\rho gh$
$=800\times 10\times 2\times {10}^{-3}$
$=16{\text{N/m}}^2$ ..........(2)
Given, pressure due to height of oil column is equal to excess pressure of soap bubble.
From (1) and (2)
$400T=16$
$\Rightarrow T=0.04\text{N/m}$