Two vertical parallel glass plates are partically 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 the wetting is complete. Find the force of their mutual attraction

Explanation

The energy of the liquid between the plates is
`E = l d h rho g ((h)/(2)) - 2 alpha l h = (1)/(2) rho gl dh^2 - 2 alpha l h`
=`(1)/(2) rho g l d (h -(2 alpha)/(rho g d))^2 - (2 alpha^2 l)/(rho g d)`
This energy is minimum when, `h = (2 alpha)/(rho g d)` and
the minimum potential energy is then `E_(min) = -(2 alpha^2 l)/(rho g d)`
The force of attraction between the plates can be obtained from this as `F = (- del E_(min))/(del d) = -(2 alpha^2 l)/(rho g d^2)`(minus sign means the force is attractive.)
Thus `F = -(alpha l h)/(d) = 13 N`.
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