"Any body that is completely or partially submerged in a fluid (gas or liquid) at rest is acted upon by an upward or buoyant force, the magnitude of which is equal to the weight of the fluid displaced by the body." Which is this law?

Archimedes' Principle

The correct answer is option 3. Archimedes' Principle.

Archimedes' Principle, formulated by the ancient Greek mathematician and scientist Archimedes, is a fundamental principle in fluid mechanics. It states that when an object is immersed either partially or fully in a fluid (liquid or gas) at rest, it experiences an upward buoyant force that is equal in magnitude to the weight of the fluid displaced by the object.

Here's a breakdown of the key components of Archimedes' Principle:

1. Buoyant Force:

When an object is submerged in a fluid, it displaces some of the fluid. The surrounding fluid exerts an upward force on the object, known as the buoyant force.

This buoyant force arises due to the pressure difference between the top and bottom surfaces of the submerged object. The pressure at the bottom is higher than at the top, resulting in a net upward force.

2. Magnitude of the Buoyant Force:

The magnitude of the buoyant force is equal to the weight of the fluid displaced by the submerged object. This principle is encapsulated in the famous statement attributed to Archimedes: "Eureka!," meaning "I have found it!"

Mathematically, the buoyant force (\(F_b\)) is given by \(F_b = \rho \cdot V \cdot g\), where:

\(\rho\) is the density of the fluid,

\(V\) is the volume of fluid displaced by the object,

\(g\) is the acceleration due to gravity.

3. Effect on Buoyancy:

Objects with a density less than that of the fluid (i.e., less dense than the fluid) experience a net upward buoyant force, causing them to float.

Objects with a density greater than that of the fluid (i.e., denser than the fluid) experience a net downward force, causing them to sink.

4. Applications:

Archimedes' Principle finds widespread applications in various fields, including shipbuilding, engineering, and hydrodynamics.

It explains why ships and boats float, how hot air balloons rise, and why certain objects appear lighter when submerged in water.

In summary, Archimedes' Principle is a fundamental concept in fluid mechanics, stating that the buoyant force experienced by an object immersed in a fluid is equal to the weight of the fluid displaced by the object. It provides insight into the behavior of submerged objects and has practical applications in various scientific and engineering contexts.