Concept — Centre of pressure: The centre of pressure (CP) is the single point at which the entire resultant hydrostatic force on a submerged surface can be considered to act. Its location depends on how the fluid pressure is distributed over the surface. Since gauge pressure at any point in a static fluid is p = ρgh (proportional to depth h below the free surface), the pressure distribution — and therefore the CP — is governed entirely by how the depth varies across the surface.

Why the horizontal case is special: For a horizontal plane surface, every point of the area lies at exactly the same depth. Hence the pressure is uniform over the whole surface. A uniform pressure distribution has its resultant acting exactly at the centroid (the geometric centre) of the area — just as a uniformly distributed load on a plate acts through the plate's centroid. Therefore, for a horizontal surface the centre of pressure coincides with the centroid, which is why the choice describing it as the centroid representing the geometric centre of the area is correct.

Why the other options are wrong:

• The statement that CP lies below the centroid when the surface is inclined is a true fact in general, but it does not describe the horizontal case that the question specifically asks about — for a horizontal surface there is no depth variation, so the CP does not shift below the centroid.
• The top edge answer is incorrect because the resultant of a uniform pressure cannot act at a boundary; it must act through the area's balance point, the centroid.
• The claim that CP is independent of depth of immersion is misleading — for inclined/vertical surfaces the CP position relative to the centroid changes with depth (the term I/(A·h̄) decreases as depth increases), so CP is generally not depth-independent.

General formula for reference: For an inclined surface the CP depth is h_CP = h̄ + I_G·sin²θ / (A·h̄). For a horizontal surface θ = 0, the extra term vanishes, and h_CP = h̄, i.e. the CP sits at the centroid.