According to Archimedes’ principle, the magnitude of the buoyant force acting on a body immersed in a fluid depends primarily on which physical property of the fluid?

Introduction / Context:

This general physics question is about Archimedes’ principle and the concept of buoyant force. When an object is partly or completely immersed in a fluid such as water or air, it experiences an upward force called the buoyant force. Understanding which property of the fluid this buoyant force depends on helps students apply the principle correctly in problems related to floating, sinking, and fluid mechanics.

Given Data / Assumptions:

• An object is immersed in a fluid (for example, water or oil).
• The fluid has a definite density, mass, volume, and temperature.
• We are interested only in which property of the fluid determines the magnitude of the buoyant force.
• Standard form of Archimedes’ principle is assumed: buoyant force equals weight of displaced fluid.

Concept / Approach:

According to Archimedes’ principle, the buoyant force on an immersed body is equal to the weight of the fluid displaced by that body. Weight of the displaced fluid is given by the product of fluid density, displaced volume, and acceleration due to gravity. Therefore, the magnitude of the buoyant force depends directly on the density of the fluid and the volume displaced, along with the constant g. The question specifically asks about a property of the fluid itself, so density is the relevant choice among the given options.

Step-by-Step Solution:

Verification / Alternative check:

Consider placing the same object in water and in a lighter fluid such as kerosene. The object may float higher or lower depending on the fluid. Water has higher density than kerosene, so it provides a greater buoyant force for the same displaced volume. This practical observation matches the formula, confirming that density is the key fluid property that affects the buoyant force magnitude.

Why Other Options Are Wrong:

• Mass: The total mass of the fluid in the container does not by itself determine buoyant force on the object; local displaced volume and density matter more.
• Temperature: Temperature can change density, but buoyant force is not expressed directly in terms of temperature. It is an indirect factor, not the primary property in the formula.
• Volume: Fluid volume in the container is not the controlling factor. The volume of fluid displaced by the body matters, but that is not a property of the fluid itself.

Common Pitfalls:

Students sometimes confuse the volume of the object or the volume of the container with a fluid property. Others focus on temperature because they know density varies with temperature, but they overlook that the formula is written directly in terms of density. Remember that in Archimedes’ principle, the buoyant force is directly proportional to fluid density for a given displaced volume.

Final Answer:

The magnitude of the buoyant force depends on the density of the fluid.