Question

A soap bubble is being blown at the end of a very narrow tube of radius $b$. Air (density $\rho$) moves with a velocity ${}^{\prime }{v}^{\prime }$ inside the tube and comes to rest inside the bubble. The surface tension of the soap solution is $T$. After some time the bubble, having grown to a radius ${}^{\prime }{r}^{\prime }$ separates from the tube. Find the value of ${}^{\prime }{r}^{\prime }$. Assume that $r>>b$ so that you can consider the air to be falling normally on the bubble's surface.

• A. $\frac{4T}{P{v}^2}$
• B. $\frac{4T}{Pv}$
• C. $\frac{2T}{P{v}^2}$
• D. $\frac{4T}{P{v}^3}$

Answer 1

The correct option is A $\frac{4T}{P{v}^2}$

Pressure due to moving air $=\rho v^2$

Excess pressure inside the bubble = $\frac{\text{4T}}{\text{r}}$

The bubble will separate from the tube whey $\rho v^2=\frac{4T}{r}$

$r=\frac{4T}{\rho v^2}$