A soap bubble of radius `'r'` and surface tension `'T'` is given a potential of `'V'` volt. If the new radiys `'R'` of the bubble is related to its initial radius by equation.
`P_(0)[R^(3) - r^(3)] + [lambda T [R^(2) - r^(2)] - epsilon_(0) V^(2)R//2 = 0`, where `P_(0)` is the atmospheric pressure. Then find `lambda`

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 )`.