There is an air bubble of radius 1.0 mm in a liquid of surface tension 0.075 and density 1000 at a depth of 10 cm below the free surface. [2023]

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Solution

Q.
There is an air bubble of radius 1.0 mm in a liquid of surface tension 0.075 ${Nm}^{- 1}$ and density 1000 ${kg m}^{- 3}$ at a depth of 10 cm below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is ________ Pa $(g = 10 {ms}^{- 2})$ [2023]

Ans.
(1150)

$Pressure inside the bubble$

$P = P_{0} + h ρ g + \frac{2 T}{r}$

$P - P_{0} = h ρ g + \frac{2 T}{r}$

$= 0.1 \times 1000 \times 10 + \frac{2 \times 0.075}{10^{- 3}}$

$= 1000 + (0.1) (1000)$ $= 1150 Pa$

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