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 liquids is $T$ and angle of contact is $\theta$, then 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

Answer: (B)

Let the width of each plate is $b$ and due to surface tension, liquid will rise upto height $h$. Then upward force due to surface tension $=2Tb\cos \theta$ ...(i)

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