A rigid square sheet of size $$2\,\text{m} \times 2\,\text{m}$$ is hinged at the middle of the vertical edges to serve as a door which can turn about the horizontal axis $$OO'$$. A fluid of density $$\rho$$ fills the space to the left of the sheet up to its top. The horizontal force $$F$$ required, to be applied at the lower edge, to hold the sheet vertical is

A

$$\frac{2}{3}\rho g$$

B

$$\frac{4}{3}\rho g$$

C

$$\frac{8}{3}\rho g$$

D

$$\frac{1}{3}\rho g$$