1. 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 P, the liquid surface makes angle0.(0o <<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 \(\theta \left(\text{x} \right)\,=\, sin\theta \left(\text{x} \right)\,=\,tan\theta \left(\text{x} \right)\,=\, \frac{\text{dy}}{\text{dx}} \text{, g}\) is the acceleration due to gravity)

(1).\(\displaystyle \frac{\text{dy}}{\text{dx}}\,=\, \sqrt{\frac{\rho\text{g}}{\text{S}}x}\)

(2). \(\displaystyle \frac{\text{d}^2\text{y}}{\text{dx}^2}\,=\, \frac{\rho \text{g}}{\text{S}}x\)

(3). \(\displaystyle \frac{\text{d}^2\text{y}}{\text{dx}^2}\,=\, \frac{\rho \text{g}}{\text{S}}y\)

(4). \(\displaystyle \frac{\text{d}^2\text{y}}{\text{dx}^2}\,=\, \sqrt{\frac{\rho \text{g}}{\text{S}}}\)