Question

An air bubble of radius $1mm$ is located at a depth of $20cm$ below water level. The excess pressure inside the bubble above the atmospheric pressure is [Given, the surface tension of water is $0.075N{m}^{-1}$ and density is $1000kg{m}^{-3}$ ]

• A. $2110Pa$
• B. $2210Pa$
• C. $2260Pa$
• D. $2310Pa$

Answer 1

Answer: (A)

Let the atmospheric pressure be $P_0$
Pressure just outside the bubble,
$P=P_0+h\rho g$
Pressure of air inside the bubble
$P_{in}=R+\frac{2\sigma }{r};\sigma$ is surface tension
$P_{in}=P_0+h\rho g+\frac{2\sigma }{r}$
$\therefore P^{{}^{\prime }}-P_0=\frac{1}{5}\times 1000\times 9.8+\frac{2\times 0.075}{1\times 10^{-3}}$
$=1960+150$
$=2110Pa$