MHT CET · Physics · Mechanical Properties of Fluids

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

A \(\frac{F V}{2 A^2}\)
B \(\frac{\mathrm{A}^2}{\mathrm{FV}}\)
C \(\frac{\mathrm{AV}}{\mathrm{F}^2}\)
D \(\frac{\mathrm{FV}}{4 \mathrm{~A}^2}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{F V}{2 A^2}\)

Step-by-step Solution

Detailed explanation

Consider complete wetting.

The Laplace pressure jump is given by:
\(\Delta P =\frac{ T }{( R )}=\frac{ F }{ A }\quad\ldots(1)\)
On considering volume conservation: \(\frac{4}{3} \pi r^3=V \approx A(2 R)\)
\(\therefore R \approx \frac{ V }{2 A}\quad\ldots(2)\)
On plugging into equation (1), \(\frac{\mathrm{T}}{\left(\frac{\mathrm{V}}{2 \mathrm{~A}}\right)}=\frac{\mathrm{F}}{\mathrm{A}}\)
\(\therefore \mathrm{T}=\frac{\mathrm{FV}}{2 \mathrm{~A}^2}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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