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 an angle $\theta_0 \left(\theta_0 \ll 1\right)$ with the $x$-axis at $x=L$. If $y(x)$ is the height of the surface,then the equation for $y(x)$ is:
(Take $\theta(x) \approx \sin \theta(x) \approx \tan \theta(x) = \frac{dy}{dx}$,where $g$ is the acceleration due to gravity.)

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