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A bubble having surface tension T and ra...

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.

A

1. `(2T)/(rhov^(2))`

B

2. `(2T)/(rhov)`

C

3. `(4T)/(rhov^(2))`

D

4. `(4T)/(rhov)`

Text Solution

Verified by Experts

The correct Answer is:
C
Excess pressure inside a bubble `=(4T)/(R)`
Let area of bubble at wall where air strikes be A.
`therefore` Force due to excess pressure`=(4TA)/(R)`
Let `rho=`density of air, Force due to striking air`=rhoAv^(2)`
For bubble to separate from the ring,

`rhoAv^(2)` or `rhoAv^(2)R=4TA` or `R=(4T)/(rhov^(2))`
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