Question

Two vertical parallel glass plates are partially submerged in water. The distance between the plates is $d$ and the length $l$. Assume that the water between the plates does not reach the upper edges of the plates and that the wetting is complete. Calculate the force of attraction between the plates. ($\rho =$density of water and $\sigma =$ surface tension of water)
Here $h$ represents the height to which the liquid rises.

• A. $\frac{l\rho g}{2}{h}^2$
• B. $\frac{l\rho g}{2}h$
• C. $\frac{l\rho g}{2}$
• D. $\frac{l\rho g}{2h}$

Answer 1

The correct option is A $\frac{l\rho g}{2}{h}^2$

Work done in separating the plates should be equal to rise in Potential energy to raise the water to height $h$.

Since the center of mass of water is at height $h/2$

$WorkDone=\rho g\left(h/2\right)\times \left(hld\right)$

If $F$ the force of attraction then,

$Fd=\rho g\left(h/2\right)\times \left(hld\right)$

So $F=\frac{l\rho g}{2}{h}^2$