A soap bubble of radius r and surface tension T is given a potential V. Show that the new radius R of the bubble is related with the initial radius by the equation
`P(R^(3) -r^(3)) +4T (R^(2)-r^(2)) = (in_(0)V^(2)R)/(2)` where P is the atmospheric pressure.

Answer

A

Explanation

`p_(1)V_(1)=p_(2)V_(2)`
`:. (p_(0)+(4T)/(r ))((4)/(3) pi r^(3))=(p_(0)+(4T)/(R)-(sigma^2)/(2 epsilon_(0))) ((4)/(3) piR^(3))`
Here, `V=(sigmaR)/(epsilon_(0))`
or, `sigma=(V epsilon_(0))/(R )`.