Question

What should be the pressure inside a air bubble of radius $0.1\text{mm}$ situated $1\text{m}$ below the water surface?
(Take surface tension of water $T=7.2\times {10}^{-2}\text{N/m}$ and $g=10{\text{m/s}}^2$)

• A. $3.5\times {10}^5\text{Pa}$
• B. $1.11\times {10}^5\text{Pa}$
• C. $2.11\times {10}^5\text{Pa}$
• D. $3\times {10}^5\text{Pa}$

Answer 1

The correct option is B $1.11\times {10}^5\text{Pa}$

For air bubble, $r=0.1\text{mm}=0.1\times {10}^{-3}\text{m}={10}^{-4}\text{m}$
Depth of bubble below the water's surface is $h=1\text{m}$
Surface tension of water, $T=7.2\times {10}^{-2}\text{N/m}.$


Pressure at depth $h$,
$P_1=P_0+\rho gh$
$P_1={10}^5+(1000\times 10\times 1)...\left(i\right)$
Applying equation for excess pressure for air bubble:
$P_2-P_1=\frac{2T}{r}...\left(ii\right)$
$\because P_2$ being on the concave side of bubble, it is higher than $P_1$.


From Eq $\left(i\right)\&\left(ii\right)$,
$P_2-({10}^5+(1000\times 10\times 1\left)\right)=\frac{2\times 7.2\times {10}^{-2}}{{10}^{-4}}$
$P_2=1.1\times {10}^5+(0.01\times {10}^5)$
$\therefore P_2=1.11\times {10}^5\text{Pa}$
The pressure inside air bubble is $1.11\times {10}^5\text{Pa}$