When a body is submerged in a fluid, it experiences forces from the surrounding fluid pressure and from gravity. Let's consider the forces acting on two scenarios:

Forces on a Solid Submerged Body

A solid body submerged in a fluid is subjected to two main forces:

• Weight: The force of gravity acting downwards, equal to the mass of the solid body multiplied by the acceleration due to gravity ($\text{W}_{\text{solid}} = \text{m}_{\text{solid}} \times \text{g}$).
• Buoyant Force: The upward force exerted by the fluid, which is the resultant of the pressure forces acting on the surface of the body. Pressure in a fluid increases with depth, so the pressure on the bottom surface of the body is greater than the pressure on the top surface, resulting in a net upward force. This buoyant force is equal to the weight of the fluid displaced by the body ($\text{F}_{\text{B}} = \text{Weight of displaced fluid}$).

Forces on a Fluid Body of the Same Shape and Depth

Now consider an imaginary volume of fluid within the larger fluid, having the exact same shape and located at the same depth as the solid body. This fluid body is in equilibrium within the surrounding fluid. The forces acting on this fluid body are:

• Weight: The force of gravity acting downwards on this specific volume of fluid ($\text{W}_{\text{fluid}} = \text{m}_{\text{fluid}} \times \text{g}$).
• Buoyant Force: The upward force exerted by the surrounding fluid pressure on the surface of this fluid volume. Since this fluid volume is in equilibrium (not accelerating), the buoyant force acting on it must be equal to its weight. Thus, the buoyant force on the fluid body equals the weight of the fluid body.

Comparing the Forces

The buoyant force in both cases arises from the pressure distribution of the surrounding fluid on the surface of the body. For both the solid body and the imaginary fluid body of the same shape at the same depth, the surrounding fluid is the same, the shape is the same, and the depth is the same. Therefore, the pressure distribution on the surface of both bodies is identical.

Since the pressure distribution is the same and the surface area is the same, the resultant force due to this pressure distribution – the buoyant force – is identical for both the solid submerged body and the fluid body of the same shape and depth.

The weight of the solid body ($\text{W}_{\text{solid}}$) and the weight of the fluid body of the same volume ($\text{W}_{\text{fluid}}$) are generally different unless the solid has the same density as the fluid. However, the question asks about the forces acting on the body, and the buoyant force (the force exerted by the fluid pressure) is one of these forces.

The forces exerted by the fluid on the surface of the solid body are identical to the forces exerted by the fluid on the surface of the fluid body of the same shape and depth. These forces result in the buoyant force, which is identical in both scenarios.

Conclusion

The buoyant force acting on a solid submerged body is identical to the buoyant force acting on a fluid body of the same shape at the same depth. This is because the buoyant force is determined by the pressure distribution of the surrounding fluid, which is the same for identical shapes at the same depth in the same fluid.

Therefore, the forces acting on a solid submerged body in a fluid and on a fluid body of the same shape at the same depth are always identical, specifically referring to the buoyant force component which arises from the fluid pressure.