An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having surface tension $0.095 \mathrm{~J} / \mathrm{m}^2$ and density $10^3 \mathrm{~kg} / \mathrm{m}^3$. The difference between pressure inside the bubble and atmospheric pressure is _____…

Question

An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having surface tension $0.095 \mathrm{~J} / \mathrm{m}^2$ and density $10^3 \mathrm{~kg} / \mathrm{m}^3$. The difference between pressure inside the bubble and atmospheric pressure is _____ $\mathrm{N} / \mathrm{m}^2$. (Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$)

Aicharya · Accepted Answer

$\Delta \mathrm{P}=\mathrm{P}_{\mathrm{in}}-\mathrm{P}_0$
$\begin{aligned} & =\rho \mathrm{gh}+\frac{2 \mathrm{~T}}{\mathrm{R}}=\frac{1000 \times 10 \times 20}{100}+\frac{2 \times 0.095}{10^{-3}} \\ & =2000+190 \\ & =2190\end{aligned}$

An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having…

Solution