Inclined Plane Submerged in a Liquid and Its Centre of Pressure

When an inclined plane is submerged in a liquid, certain forces act on it due to the pressure exerted by the liquid. These forces result in a center of pressure being formed on the plane. The center of pressure refers to the point where the total pressure force acts on the plane.

Explanation of the Correct Answer: Option C
The correct answer is option C, which states that the center of pressure is below the center of gravity. Let's understand why this is the case.

Inclined Plane and Pressure Distribution
When an inclined plane is submerged in a liquid, the pressure distribution on the plane is not uniform. The pressure increases with depth due to the weight of the liquid column above it. The pressure at any point on the inclined plane can be calculated using the hydrostatic pressure equation:

P = ρgh

Where:
P = pressure at a point
ρ = density of the liquid
g = acceleration due to gravity
h = depth from the liquid surface to the point

Center of Pressure and Resultant Force
The center of pressure can be defined as the point through which the resultant force acts on the inclined plane. This resultant force is a combination of the pressure forces acting on different areas of the plane.

When the inclined plane is submerged in a liquid, the pressure forces on different areas of the plane are not balanced. As a result, a net force acts on the plane, which can be resolved into two components: the normal force and the parallel force.

Location of the Center of Pressure
The location of the center of pressure depends on the shape and orientation of the inclined plane. For a submerged inclined plane, the center of pressure is below the center of gravity. This means that the net force acts below the center of gravity, causing a moment that tends to rotate the plane.

The reason behind this is the non-uniform pressure distribution on the inclined plane. The pressure increases with depth, so the pressure forces acting on the lower portion of the plane are greater than those acting on the upper portion. This creates a net force that is not aligned with the center of gravity, resulting in a downward shift of the center of pressure.

Conclusion
In conclusion, when an inclined plane is submerged in a liquid, the center of pressure is below the center of gravity. This is because the pressure forces acting on the lower portion of the plane are greater than those acting on the upper portion, resulting in a net force that is not aligned with the center of gravity. Understanding the location of the center of pressure is important for analyzing the stability and equilibrium of submerged objects.