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

Answer 1

Answer: (C)

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 $=\frac{4 TA}{R}$
Let $ \rho=$ density of air, Force due to striking air $=\rho Av^{2}$ For bubble to separate from the ring,

$\rho AV^{2}=\frac{4TA}{R}$ or $\rho Av^{2}R=4TA $
or $ R=\frac{4T}{\rho v^{2}} .$