A water drop of radius ' $r$ ' and volume ' $\mathrm{V}$ ' is kept in between the two identical glass plates…

A water drop of radius ' $r$ ' and volume ' $\mathrm{V}$ ' is kept in between the two identical glass plates such that it forms a thin layer of area ' $\mathrm{A}$ ' between the plates. A force ' $\mathrm{F}$ ' is applied such that the two plates separate from each other. The surface tension ' $\mathrm{T}$ ' of the liquid is
  1. $\frac{F V}{2 A^2}$
  2. $\frac{\mathrm{A}^2}{\mathrm{FV}}$
  3. $\frac{\mathrm{AV}}{\mathrm{F}^2}$
  4. $\frac{\mathrm{FV}}{4 \mathrm{~A}^2}$

Solution

Consider complete wetting. The Laplace pressure jump is given by: On plugging into equation (1), $\frac{\mathrm{T}}{\left(\frac{\mathrm{V}}{2 \mathrm{~A}}\right)}=\frac{\mathrm{F}}{\mathrm{A}}$ $\therefore \mathrm{T}=\frac{\mathrm{FV}}{2 \mathrm{~A}^2}$

Asked in: MHT CET 2022 (07 Aug Shift 1)

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