Question

Two coaxial cylinders made of glass are immersed in a liquid of surface tension $‘S^{\prime }$. Radii of inner and outer cylinders are $R_1$ and $R_2$ respectively. Height till which the liquid will rise between the walls of the cylinder is:- (Density of liquid is $\rho$ and assume angle of contact to be $0^{\circ }$)

• A. $\frac{2S}{R_2\rho g}$
• B. $\frac{2S}{R_1\rho g}$
• C. $\frac{S}{(R_2-R_1)\rho g}$
• D. $\frac{2S}{(R_2-R_1)\rho g}$

Answer 1

The correct option is D $\frac{2S}{(R_2-R_1)\rho g}$

Assuming angle of contact to be $0^{\circ }$, the surface tension force will act vertically upwards at the walls of the cylinder.

Net surface tension force will balance the weight of the liquid column which rises.
i.e $2\pi R_{1}S+2\pi R_{2}S=$ Weight of liquid column
$2\pi S(R_1+R_2)=(\pi R_2^{2}h-\pi R_1^{2}h)\rho g$
$\Rightarrow 2S(R_1+R_2)=h(R_2^2-R_1^2)\rho g$
$\Rightarrow 2S(R_1+R_2)=h(R_2-R_1)(R_1+R_2)\rho g$
or $h=\frac{2S}{(R_2-R_1)\rho g}$