Determine the force exerted by the water on a 2 m^2 plane surface...

The pressure at a depth $h$ in a fluid is given by $P = \rho g h$.

Substituting the given values, $P = 1000 \times 10 \times 500 = 5 \times 10^6 \text{ N/m}^2$.

The magnitude of the force exerted on the surface is $F = P \times A$.

$F = 5 \times 10^6 \times 2 = 10^7 \text{ N}$.

Since pressure in a fluid at rest is isotropic (acts equally in all directions), the magnitude of the force depends only on the depth and the area of the surface. It does not depend on the orientation of the surface.