Physics · PYQ NEET UG 2025

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)

1. \( \frac{d^2y}{dx^2} = \frac{\rho g}{S} x \)
2. \( \frac{d^2y}{dx^2} = \frac{\rho g}{S} y \)
3. \( \frac{d^2y}{dx^2} = \sqrt{\frac{\rho g}{S}} \)
4. \( \frac{dy}{dx} = \sqrt{\frac{\rho g}{S}} x \)