A water tank with wall at x=L, liquid of surface tension S and density rho. Liquid surface height y(x) satisfies which equation? (Given theta(x)approxtantheta=frac dy dx ):

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NEET Physics QUESTION #1066

Question 1

A water tank with wall at \(x=L\), liquid of surface tension \(S\) and density \(\rho\). Liquid surface height \(y(x)\) satisfies which equation? (Given \(\theta(x)\approx\tan\theta=\frac{dy}{dx}\)):

d²y/dx² = √(ρg/S)
dy/dx = √(ρg/S)·x
d²y/dx² = (ρg/S)x
d²y/dx² = (ρg/S)y✔️

Correct Answer Explanation

The meniscus shape is governed by the balance between surface tension (curvature force) and hydrostatic pressure. The capillary equation gives: \(\frac{d^2y}{dx^2} = \frac{\rho g}{S}y\). This is the standard capillary length equation where the curvature \(\approx d^2y/dx^2\) for small angles equals \(\rho g y/S\).

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