Question

A tube of fine bore AB is connected to a manometer M as shown. The stopcock S controls the flow of air AB is dipped into a liquid whose surface tension is $\sigma$. On opening the stopcock for a while a bubble is formed at B and the manometer level is recorded showing a difference h in the levels in the two arms if P be the density of manometer liquid and r the radius of curvature of the bubble then the surface tension $\sigma$ of the liquid is given by

• A. $\rho hrg$
• B. $2\rho hrg$
• C. $4\rho hrg$
• D. $\frac{rh\rho g}{4}$

Answer 1

The correct option is D $\frac{rh\rho g}{4}$

Surface tension of liquid $=\sigma$

Difference in pressure $=P$

Radius of curvature of manometer $=r$

Equating difference in pressure from Bernoulli's law:

$\Delta P=\frac{4\sigma }{r}=\rho gh$

$\Rightarrow \sigma =\frac{\rho hrg}{4}$