First slide

Surface tension

Question

The pressure inside a small air bubble of radius 0.1 mm situated just below the surface of water will be equal to [Take surface tension of water $70 \times 10^{- 3} {Nm}^{- 1}$ and atmospheric pressure = $1.013 \times 10^{5} {Nm}^{- 2}$ ]

Moderate

A

$2.954 \times 10^{3} Pa$
B

$1.027 \times 10^{3} Pa$
C

$1.027 \times 10^{5} Pa$
D

$2.054 \times 10^{5} Pa$

Solution

Excess pressure inside the air bubble = $\frac{2 T}{r}$
$\Rightarrow P_{in} - P_{out} = \frac{2 T}{r} = \frac{2 \times 70 \times 10^{- 3}}{0.1 \times 10^{- 3}} = 1400 Pa$
$\Rightarrow P_{in} = 1400 + 1.013 \times 10^{5}$
= $0.014 \times 10^{5} + 1.013 \times 10^{5} = 1.027 \times 10^{5} Pa$

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