What is the excess pressure inside a bubble of soap solution of radius 5.00mm, given that the surface tension of soap solution at the temperature `(20^(@)C)` is `2.50xx10^(-2)Nm^(-1)`? If an air bubble of the same dimension were formed at a depth of 40.0 cm inside a container containing the soap solution (of relative density 1.20), what would be the pressure inside the bubble? (1atm. is `1.01 xx 10^(5)Pa`).
Text Solution
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Here, `T = 2.5 xx10^(-2) Nm^(-1)` `r = 5.00 mm = 5 xx 10^(-3) m ` Density of soap solution , ` rho = 1.2 xx10^(3) kgm^(-3)` Excess pressure inside the soap bubble , `rho = (4T)/r = (4xx2.5 xx10^(-2))/(5xx10^(-3)) = 20 ` Pa Excess pressure inside the air bubble, `rho. = (2T)/r = (2xx 2.5 xx10^(2))/(5xx10^(-3)) = 10 Pa` Total pressure inside the air bubble at depth h in soap solution = p. + atmospheric pressure + `h rho g ` ` = 10 + 1.01 xx 10^(5) + 0.4 xx1.2 xx10^(3) xx 9.8 ` ` = 1.06 xx10^(5) Pa`
In question number 88, if an air bubble of the same dimensions were formed at a depth of 30 cm inside a container containing the soap solution of relative density 1.20, then the pressure inside the bubble is ( Take 1 atm = 1.01 xx 10^(5) Pa)
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FIITJEE-FLUID MECHANICS -ASSIGHNMENT COMPREHENSION NUMERICAL BASED QUESTIONS
