Question

Two parallel glass plates are dipped partialy in the liquid of density $d$ keeping them vertical. If the distance between the plates is $x$, surface tension for liquid is $T$ and angle of contact is $\theta$ then the rise of liquid between the plates due to capillary 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 upto height $h$.

Upward force due to surface tension $=2Tb\cos \theta ...\left(i\right)$

Weight of the liquid that rises in between the plates
$=Vdg=\left(bxh\right)dg....\left(ii\right)$
Equating Eqs. $\left(i\right)$ and $\left(ii\right)$ we get,
$2Tb\cos \theta =bxhdg$
$\therefore h=\frac{2T\cos \theta }{xdg}$

Hence, $\left(B\right)$ is the correct answer.