What is the excess pressure inside a bubble of soap solution of radius `5.00` mm, given that the surface tension of soap solution at the temperature `(20^(@)C)` is `2.50xx10^(-2)Nm^(-1)` ? If an air bubbled of the same dimension were formed at depth of `40.00` cm inside a container containing the soap solution (of relative density `1.20`), what would be the pressure inside the bubble ? ( `1` atmospheric pressure is `1.01xx10^(5)` Pa).

Explanation

Here, `S=2.5xx10^(-2)Nm^(-1), r=5.00mm=5xx10^(-3)m`
Density of soap solution, `rho=1.2xx10^(3)kgm^(-3)` Excess pressure inside the soap bubble, `P=(4s)/(r)=(4xx2.5xx10^(-2))/(5xx10^(-3))=20` Pa
Excess pressure inside the air bubble, `P.=(2S)/(r)`
`=(2xx2.5xx10^(-2))/(5xx10^(-3))=10` Pa
Total pressure inside the air bubble at depth h in soap solution = `rho.+` atmospheric pressure `+` hrhog
`=10+1.01xx10^(5)+0.4xx1.2xx10^(3)xx9.8`
`=1.06xx10^(3)` Pa