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

Answer

`04.00`

Explanation

Excess pressure inside a bubble `=(4T)/R`
Let area of wall of bubble where air strikes be A.

`:.` Force due to excess pressure `= (4TA)/R`
Now, force due to striking air `= rho Av^2`
For bubble to separate from the ring.
`p Av^2 = (4TA)/R implies R = (4T)/(rhov^2)`
`implies Z = 4`