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Surface Tension

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2025 1 question

Consider a water tank shown in the figure. It has one wall at $x = L$ and can be taken to be very wide in the $z$ direction. When filled with a liquid of surface tension $S$ and density $\rho$, the liquid surface makes angle $\theta_{0} (\theta_{0} \ll 1)$ with the $x$-axis at $x = L$. If $y(x)$ is the height of the surface then the equation for $y(x)$ is:(take $\theta(x) = \sin\theta(x) = \tan\theta(x) = \frac{dy}{dx}$, $g$ is the acceleration due to gravity)

2024 1 question

A thin flat circular disc of radius 4.5 cm is placed gently over the surface of water. If surface tension of water is 0.07 N m$^{-1}$, then the excess force required to take it away from the surface is;