A bubble having surface tension T and radius R is formed on a ring of radius `b(b lt lt R)`. Air is blown inside the tube with velocity v as shown. The air molecule collides perpendicularly with the wall of the bubble and stops. Calculate the radius at which the bubble separates from the ring.

Options

A. `(4T)/(rhov^(3))`
B. `(4T)/(rhov)`
C. `(2T)/(rhov^(2))`
D. `(4T)/(rhov^(2))`

Answer

D

Explanation

The bubble will separate from the tube when thrust force exerted by the air is equal to the force due to excess pressure.
`i.e., rhoAv^(2)=((4T)/(r))A or r=(4T)/(rhov^(2))`