Question

Two vertical parallel glass plates are partially submerged in water. The distance between the plates is $d=0.10mm$, and their width is $l=12cm$. Assuming that the water between the plates does not reach the upper edges of the plates and that the wetting is complete, find the force of their mutual attraction.

• A. $17N$
• B. $13N$
• C. $10$
• D. $19N$

Answer 1

The correct option is B $13N$

$Given:$ $d=0.10mm$ ; $l=12cm$

$Solution:$ The energy of the liquid between the

plates is

$E=ldh\rho g\frac{h}{2}-2\alpha lh$

$=\frac{1}{2}\rho gld{h}^2-2\alpha lh$

$=\frac{1}{2}\rho gld{(h-\frac{2\alpha }{\rho gd})}^2-\frac{2{\alpha }^{2}l}{\rho gd}$

This energy is minimum when,

$h=\frac{2\alpha }{\rho gd}\text{and}$

the minimum potential energy is then $E_{min}$

$=-\frac{2{\alpha }^{2}l}{\rho gd}$

The force of attraction between the

plates can be obtained from this as

$F=\frac{-\partial E_{min}}{\partial d}=-\frac{2{\alpha }^{2}l}{\rho g{d}^2}$

$

(minus sign means the force is attractive.)

Thus

$F=-\frac{\alpha lh}{d}=13N$

$So,the$ $correct$ $option:B$