Question

Two parallel glass plates are dipped partly in the liquid of density $d$ keeping them vertical. If the distance between the plates is $x$, surface tension of liquid is $T$ and angle of contact is $\theta$, then the rise of liquid between the plates due to capillarity will be

• A. $\frac{T\cos \theta }{xd}$
• B. $\frac{2T\cos \theta }{xdg}$
• C. $\frac{2T}{xdg\cos \theta }$
• D. $\frac{T\cos \theta }{xdg}$

Answer 1

The correct option is B $\frac{2T\cos \theta }{xdg}$

Let the width of each plate is $b$ and due to surface tension liquid will rise up to height $h$, then,

upward force due to surface tension $=2Tb\cos \theta ---\left(1\right)$


The weight of the liquid rises in between the plates
$=Mg=Vdg=\left(bxh\right)dg---\left(2\right)$

At equilibrium, net force acting on the system is zero,

Equating equations $\left(1\right)\text{and}\left(2\right)$ we get,

$2Tb\cos \theta$ = $bxhdg$

$\therefore h=\frac{2Tcos\theta }{xdg}$

Hence, option $\left(\text{B}\right)$ is correct.