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^(2))`
B. `(2T)/(rhoV^(2))`
C. `(T)/(rhoV^(2))`
D. `(2T)/(rhoV)`

Answer

A

Explanation

The bubble separates from the narrow tube, when the force due to surfacetensions is equal to force due to impact of air molecules with the wall of bubble.
`2pirxx2Tsintheta=rho(pir^(2))V^(2)`
`implies4pirT(r)/(R)=rho(pir^(2))V^(2)impliesR=(4T)/(rhoV^(2))`