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Question

(A) The pressure difference across a curved liquid surface is given by the Young-Laplace equation: $\Delta P = T \left( \frac{1}{R_1} + \frac{1}{R_2}

Vedclass · Accepted Answer

$\frac{T}{R}$

Vedclass · Answer

(A) The pressure difference across a curved liquid surface is given by the Young-Laplace equation: $\Delta P = T \left( \frac{1}{R_1} + \frac{1}{R_2} \right)$.For the cylindrical surface of water between the two plates,the two radii of curvature are $R_1 = R$ and $R_2 = \infty$ (since the surface is straight in the direction perpendicular to the cylindrical curvature).Substituting these values into the formula:$\Delta P = T \left( \frac{1}{R} + \frac{1}{\infty} \right)$Since $\frac{1}{\infty} = 0$,we get:$\Delta P = \frac{T}{R}$.However,the water film has two such interfaces (one on each side of the cylindrical meniscus),and the pressure difference is typically calculated for the entire meniscus. Given the geometry of the cylindrical surface formed between the plates,the pressure drop is $\Delta P = \frac{T}{R}$. Looking at the options provided and standard physics problems of this type,the correct expression for the pressure deficit in this specific configuration is $\frac{T}{R}$.

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