Question

A bubble having surface tension $T$ and radius $R$ is formed on a ring of radius $b(b<<R)$. Air is blown Inside the tube with velocity $v$ as shown. The air molecule collides perpendicularly with the wall of the bubble and stops. The radius at which the bubble separates from the ring is:

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

Answer 1

Answer: (C)

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

Excess pressure inside a bubble = $\frac{4T}{R}$
Let area of bubble at wall where air strikes be A.
$\therefore$ Force due to excess pressure = $\frac{4TA}{R}$
Let $\rho$ = density of air, Force due to striking air = $\rho A{v}^2$
For bubble to separate from the ring.

$\rho A{v}^2=\frac{4TA}{R}$ or $\rho A{v}^{2}R=4TAorR=\frac{4T}{\rho v^2}$