Determining Buoyant Force Magnitude

The magnitude of the buoyant force acting on an object immersed in a fluid is a fundamental concept in fluid mechanics. This force is what makes objects float or appear lighter when submerged.

Understanding Buoyant Force

Buoyant force is an upward force exerted by a fluid that opposes the weight of an immersed object. It is caused by the difference in pressure exerted by the fluid on the bottom and top surfaces of the object.

Methods to Determine Buoyant Force

Let's look at the given options to determine which principle is used to find the magnitude of the buoyant force:

• Newton’s law of viscosity: Newton's law of viscosity deals with the internal friction within a fluid when it is in motion. It describes how shear stress is related to the rate of shear strain (velocity gradient). This law is related to fluid flow and drag forces, not directly to the buoyant force.
• Archimedes’s principle: Archimedes' principle states that the buoyant force on an object immersed in a fluid is equal to the weight of the fluid displaced by the object. Mathematically, the buoyant force (\(F_B\)) can be expressed as:

  \(F_B = \rho_{fluid} \times V_{displaced} \times g\)

  Where:

  • \(\rho_{fluid}\) is the density of the fluid
  • \(V_{displaced}\) is the volume of the fluid displaced by the object (which is the volume of the submerged part of the object)
  • \(g\) is the acceleration due to gravity

  This principle provides a direct method to calculate the magnitude of the buoyant force.

• Principles of moments: Principles of moments are related to rotational equilibrium, dealing with torques (forces multiplied by distances from a pivot). While moments are important in determining stability and orientation of floating objects, they are not used to determine the magnitude of the buoyant force itself.
• None of the above: Since Archimedes' principle provides the method to determine the buoyant force, this option is incorrect.

Conclusion

Based on the analysis of the options, Archimedes' principle is the fundamental principle used to determine the magnitude of the buoyant force acting on an object immersed in a fluid. It relates the buoyant force directly to the properties of the displaced fluid.