The pressure inside an air bubble is $(200.5 + x)$ (in kN/m²) of radius 0.1mm that is located at a depth of 10m inside the water. The value of x is____.
Surface tension of water $s = 0.075 {Nm}^{- 1}$ , density of water $ρ = 10^{3} {kgm}^{- 3}$ , atmospheric pressure $P_{0} = 1.0 \times 10^{5} {Nm}^{- 2}$ and $g = 10.0 {ms}^{- 2}$ .

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Detailed Solution

19. (201.5)
Pressure at depth inside water
$P = P_{0} + eηh = 1 \times 10^{5} + 10^{3} \times 10 \times 10 = 2 \times 10^{5} {Nm}^{- 2}$
Express pressure inside air bubble
$△ P = \frac{2 s}{r} = \frac{2 \times 0.075}{0.1 \times 10^{- 3}} = 1500 {Nm}^{- 2}$
Total pressure $P + △ P = 2 \times 10^{5} \times 1500$
= 201.5 K Nm^-2