What will be the total pressure inside a spherical air bubble of radius 0.2 mm at a depth of 2m below the surface of a liquid of density `1.1 g//cm^(3)` and surface tension `50 dyn e//cm`. Atmospheric pressure is `1.01 xx 10^(5) Nm^(-2)`.

Explanation

Here, `r=0.2 mm = 0.2 xx 10^(-3) m`
`= 2 xx 10^(-4) m` ,
`h= 2m`,
`rho = 1.1 g cm^(-3) = 1.1 xx 10^(3) kg//m^(3)` ,
`S=50 dyn e//cm = 50 xx 10^(-3) N//m`
`P_(0) = 1.01 xx 10^(5) N//m^(2)`
Total pressure inside the bulb = atmospheric pressure + pressure due to column of liquid + excess of pressure
`= P_(0)+h rho g + (2S)/(r) = 1.01 xx 10^(5) + 2 xx 1.1`
`xx 10^(3) xx 9.8 + 2 z (50xx10^(-3))/(2 xx 10^(-4))`
`= 1.01 xx 10^(5) +20.58 xx 10^(3) +500`
`= 1.2158 xx 10^(5) = 1.22 xx 10^(5) N//m^(2)`.