The time of survival of a soap bubble of radius of R connected with atmosphere through a capillary of length 1 and radius r. The surface tension is T and the coefficient of viscosity of air is `eta`. In terms of `(etalR^(4))/(Tr^(4))` is

Answer

2

Explanation

The volume of air flowing per second through the capillary `V=(piPr^(4))/(8etal)` let x be the radius of the bubble at any intermediate instant t. now excess of pressure `p=(4T)/(x)` if dx is the decreae in radius of bubble in time dt the volume of air flowing out in time dt is
`dV=(pi((4T)/(x))r^(4))/(8etal)` dt the volume of bubble at radius `x=(4)/(3)pix^(3)` `becausedV=d((4)/(3)pix^(3))=4pix^(2)dx`
Hence `-4pix^(2)dx=(piTr^(4))/(2etalx)dt` o intergrating above equation we get `t=(2etalR^(4))/(Tr^(4))` answer 2