Question

A coaxial cylinder made of glass is immersed in a liquid of surface tension $S$ . The radius of the inner and outer surface of the cylinder are $R_{1}$ and $R_{2}$ respectively. Height till which liquid will rise is (Density of liquid is $\rho $ )

• A. $\frac{2 S}{R_{2} \rho g}$
• B. $\frac{2 S}{R_{1} \rho g}$
• C. $\frac{S}{\left(R_{2} - R_{1}\right) \rho g}$
• D. $\frac{2 S}{\left(R_{2} - R_{1}\right) \rho g}$

Answer 1

Answer: (D)

Net upward force
$= \, 2\pi \, R_{2}S \, + \, 2\pi R_{1} \, S \, contact \, angle=0^\circ $
$\therefore $ Capillary rise is given by
$h=\frac{2 \pi S \left(R_{1} + R_{2}\right)}{\pi \left(R_{2}^{2} - R_{1}^{2}\right) \rho g}$
$= \, \frac{2 S}{\left(R_{2} - R_{1}\right) \rho g}$