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(C) The pressure difference across a curved liquid surface is given by the Young-Laplace equation: $\Delta P = \frac{2T}{R}$,where $T$ is the surface

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(C) The pressure difference across a curved liquid surface is given by the Young-Laplace equation: $\Delta P = \frac{2T}{R}$,where $T$ is the surface tension and $R$ is the radius of curvature of the meniscus.When the capillary tube is raised by a height $h$ from its initial position,the pressure balance at the meniscus level is given by: $P_0 - \frac{2T}{R} = P_0 - \rho gh$,where $P_0$ is the atmospheric pressure,$\rho$ is the density of the liquid,and $g$ is the acceleration due to gravity.Simplifying this,we get: $\frac{2T}{R} = \rho gh$,which implies $R = \frac{2T}{\rho gh}$.This shows that $R$ is inversely proportional to $h$,i.e.,$R \propto \frac{1}{h}$.As the tube is raised ($h$ increases),the radius of curvature $R$ of the meniscus increases until it reaches the radius of the tube $r$,at which point the liquid meniscus detaches or the height reaches the equilibrium capillary rise. The graph representing $R \propto \frac{1}{h}$ is a rectangular hyperbola. Among the given options,the graph that shows $R$ decreasing as $h$ increases towards a limiting value is represented by option $C$.

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