Question

A soap bubble, having radius of $2\text{mm}$, is blown from a detergent solution having a surface tension of $5\times {10}^{-2}\text{N/m}$. Pressure inside the soap bubble is observed to be the same as the pressure at a point $h$ below the free surface of water taken in a container. Find the value of $h$.
[Take $g=10{\text{m/s}}^2$]

• A. $2\text{cm}$
• B. $4\text{cm}$
• C. $3\text{cm}$
• D. $1\text{cm}$

Answer 1

The correct option is D $1\text{cm}$

Given,
Surface Tension $\left(T\right)=5\times {10}^{-2}\text{N/m}$
Radius of soap bubble $r=2\times {10}^{-3}\text{m}$
Let us suppose pressure inside the soap bubble be $P_1$ and the pressure inside water in a container at depth $h$ is $P_2$.


We know from the definition of excess pressure inside a soap bubble,
$P_1=P_0+\frac{4T}{r}$
$\Rightarrow P_1=P_0+\frac{4\times 5\times {10}^{-2}}{2\times {10}^{-3}}=P_0+100..........\left(1\right)$
Pressure at depth $h$ in a container is given by,
$P_2=P_0+\rho gh$
$\Rightarrow P_2=P_0+1000\times 10\times h=P_0+10000h........\left(2\right)$
From the data given in the question, $P_1=P_2$
$\therefore$ from $\left(1\right)\text{and}\left(2\right)$
$P_0+100=P_0+10000h$
$\Rightarrow h=0.01\text{m}$ or $1\text{cm}$
Hence, option (d) is the correct answer.