Question

Two parallel glass plates are dipped partly in the liquid of density ${}^{\prime }{d}^{\prime }$ keeping them vertical. If the distance between the plates is ${}^{\prime }{x}^{\prime },$ 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. $\frac{2T}{xdg\cos \theta }$
• B. $\frac{T\cos \theta }{xd}$
• C. $\frac{2T\cos \theta }{xdg}$
• D. $\frac{T\cos \theta }{xdg}$

Answer 1

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

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
$=2Tb\cos \theta \dots \left(i\right)$
Weight of the liquid rises in between the plates
$=Vdg=\left(bxh\right)dg\dots \left(ii\right)$
Equating $\left(i\right)$ and $\left(ii\right)$ we get,
$2Tb\cos \theta =bxhdg$
$h=\frac{2t\cos \theta }{xdg}$
Final answer: $\left(b\right)$