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 for the liquid is $T$ and angle of contact is $\theta$, then rise of liquid between the plates due to capillary will be

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

Answer 1

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

Let
$h$ be height of liquid between the plates due to capillary action
$l$ is length of plate in contact with liquid

weight of liquid of height $\left(h\right)$ $=d\times V\times g=dxlhg$

vertical component of force due to surface tension $=T\left(2l\right)\left(cos\theta \right)$

Vertical component of force due to surface tension balances weight of the liquid

$\therefore T\left(2l\right)\left(cos\theta \right)=dxlhg$

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