Question

A soap bubble is being blown at the end of a narrow tube of diameter 2r. Air moves with a speed v inside tube and comes to rest inside bubble. Surface tension of soap solution is S and ρ is density of air. The bubble separates from tube when its radius is R. Which of the following statement is correct?

(1) R is directly proportional to r

(2) R is inversly proportional to r

(3) R is independent of r

(4) R is directly proportional to r

Answer 1

(3) R is independent of r

Fig shows tube of radius r and bubble blown at its end A of radius R. Air moves inside tube at a speed v and comes to rest inside bubble. The force exerted by air as it comes to rest at B inside bubble.

F = pAv²  ...(1)

A = area of the bubble where air strikes it. The force on area at B due to excess pressure.

\(=(\frac{4S}{R})A\)  ...(2)

The bubble is on brink of separating from tube if

From Eqn. (iii) we note, R does not depend on the radius r of the tube.