Consider a water tank as shown in the figure. It has one wall at $x=L$ and is very wide in the $z$ direction. When filled with a liquid of surface tension $S$ and density $\rho$, the liquid surface makes an 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 $\theta (x)\approx \sin \theta (x)\approx \tan \theta (x)=\frac{dy}{dx}$ and $g$ as acceleration due to gravity)

1. A
   $\frac{d^{2}y}{d{x}^2}=\frac{\rho g}{S}x$
2. B
   $\frac{d^{2}y}{d{x}^2}=\frac{\rho g}{S}y$
3. C
   $\frac{d^{2}y}{d{x}^2}=\sqrt{\frac{\rho g}{S}}$
4. D
   $\frac{dy}{dx}=\sqrt{\frac{\rho g}{S}}x$