Understanding Resultant Normal Pressure on a Body

When a body is submerged in or floating on a fluid, the fluid exerts pressure on its surface. This pressure acts perpendicular (normal) to the surface at every point. The resultant force of all these normal pressure forces acting on the entire body is a single force known as the buoyant force.

Direction of the Buoyant Force

The buoyant force arises because pressure in a fluid increases with depth. Therefore, the pressure on the lower parts of a submerged or floating body is greater than the pressure on the upper parts. This difference in pressure, when integrated over the entire surface area of the body, results in a net upward force.

This net upward force, the buoyant force, always acts vertically upward. It opposes the weight of the body and is the principle that allows objects to float or makes them feel lighter in water.

Analyzing the Options

Let's consider the given options:

• at c.g. of body: The center of gravity (c.g.) is the point where the weight of the body acts. This is generally different from where the buoyant force acts.
• at center of pressure: The center of pressure is the point where the resultant pressure force acts on a submerged *surface*. While it's related to pressure, it's not the standard term for the point of application of the resultant pressure force on an entire *body*. The resultant pressure force on a body is the buoyant force, which acts at the center of buoyancy (the centroid of the displaced fluid volume).
• vertically upward: This describes the direction of the buoyant force, which is the resultant of all normal pressure forces on a body. This is a fundamental property of buoyancy.
• at metacenter: The metacenter is a point related to the stability of floating bodies. It is not the point of application of the buoyant force itself.

Based on the properties of the buoyant force, which is the resultant of all normal pressure forces on a body, its direction is always vertically upward. While the point of application is the center of buoyancy, the option provided specifically describes the direction, which is characteristic of this resultant force.

Therefore, the most appropriate answer among the given options regarding the resultant of all normal pressure acting on a body is that it acts vertically upward.