A square gate of size 2m x 2m is hinged at its mid-point. A fluid of density $\mathrm{\sigma }$ fills the space to the left of the gate. The force F required to hold the gate stationary is:
 

• A

  $\frac{2\mathrm{\sigma g}}{3}$

• B

  $\frac{4\mathrm{g\sigma }}{3}$

• C

  $\frac{8\mathrm{\sigma g}}{3}$

• D

  $\frac{\mathrm{\sigma g}}{3}$