What should be the pressure inside a small air bubble of 0.1 mm radius situated just below the water surface? Surface tension of water is `7.2 xx 10^(-2) Nm^(-1)` and atmospheric pressure is `1.013 xx 10^(5) Nm^(-2)` .

Options

A. `2.13 xx 10^(3) Nm^(-2)`
B. `1.027 xx 10^(5) Nm^(-2)`
C. `2.5 xx 10^(5) Nm^(-2)`
D. `1.5 xx 10^(-2) Nm^(-2)`

Answer

B

Explanation

Surface tension of water `S = 7.2 xx 10^(-2) Nm^(-1)`
Radius of air bubble `R = 0.1 mm = 10^(-4) m`
The excess pressure inside tube the air bubble is given by ,
`p_(2) - p_(1) = (2S)/(R )`
`:.` Pressure inside the air bubble, `p_(2) = p_(1) + (2S)/(R )`
Substituting the values, we have
`p_(2) = (1.013 xx 10^(5)) + ((2 xx 7.2 xx 10^(-2)))/(10^(-4))`
`= 1.027 xx 10^(5) Nm^(-2)`