Understanding Archimedes Principle and Buoyant Force

Archimedes principle is a fundamental concept in fluid mechanics that explains the buoyant force experienced by an object when it is submerged in a fluid (liquid or gas). This principle was discovered by the ancient Greek mathematician and physicist Archimedes.

What is Archimedes Principle?

The principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces. This buoyant force acts upwards through the centroid of the displaced fluid.

Mathematically, the buoyant force (\(F_B\)) can be expressed as:

\(F_B = \text{Weight of displaced fluid}\)

And the weight of the displaced fluid is given by:

\(\text{Weight of displaced fluid} = (\text{mass of displaced fluid}) \times (\text{acceleration due to gravity})\)

Since mass \( = \) density \( \times \) volume, we can also write:

\(\text{mass of displaced fluid} = \rho_f \times V_{disp}\)

where:

• \(\rho_f\) is the density of the fluid
• \(V_{disp}\) is the volume of the displaced fluid (which is equal to the volume of the submerged part of the body)

So, the buoyant force is also:

\(F_B = \rho_f \times V_{disp} \times g\)

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

Analyzing the Options based on Archimedes Principle

The question asks what the upward force (buoyant force) experienced by a body immersed in a fluid is equal to, according to Archimedes principle.

Let's look at the given options:

Conclusion on the Upward Force

Based on the detailed explanation of Archimedes principle and the analysis of the options, the upward force experienced by a body immersed in a fluid is equal to the weight of the fluid displaced by the body. This principle is crucial for understanding why objects float or sink.

Revision Table: Key Concepts in Archimedes Principle

Additional Information on Buoyancy and Fluids

Understanding buoyancy is essential in various applications, from designing ships and submarines to understanding weather patterns and hot air balloons. The density of the object relative to the density of the fluid determines whether an object will float, sink, or remain suspended.

• If the density of the object is less than the density of the fluid, the object will float. The buoyant force is greater than the weight of the object if fully submerged, so it rises until the buoyant force (equal to the weight of the fluid displaced by the floating part) equals the weight of the object.
• If the density of the object is greater than the density of the fluid, the object will sink. The buoyant force when fully submerged is less than the weight of the object.
• If the density of the object is equal to the density of the fluid, the object will remain suspended at any depth within the fluid. The buoyant force when fully submerged is equal to the weight of the object.

The buoyant force always opposes gravity, acting upwards, which is why objects appear to weigh less when submerged in a fluid.