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

Introduction / Context:
When a body is placed in a fluid, it experiences an upward force called buoyant force or upthrust. Archimedes principle gives a simple rule for calculating this force and explains why objects float or sink. This question tests whether you know that the buoyant force depends on the fluid displaced, not directly on the mass of the body or the immersion depth alone.

Given Data / Assumptions:

• A body is partially or fully immersed in a liquid such as water.
• The liquid exerts an upward buoyant force on the body.
• Archimedes principle is valid: fluid is incompressible and at rest.
• We compare factors such as the mass of liquid displaced, mass of the body, depth of immersion and shape of the body.

Concept / Approach:
Archimedes principle states that the buoyant force on a body immersed in a fluid is equal to the weight of the fluid displaced by the body. Since weight equals mass multiplied by gravitational acceleration, this means that buoyancy is directly proportional to the mass of the displaced fluid, or equivalently to the volume of the displaced fluid times its density. The buoyant force does not depend directly on the mass of the body itself; a heavy object can float if it displaces enough fluid. Similarly, depth of immersion and shape affect buoyancy only through the volume of fluid displaced, not independently.

Step-by-Step Solution:
Step 1: Recall Archimedes principle: upthrust equals the weight of the fluid displaced.Step 2: Express weight as W = m * g, where m is the mass of displaced fluid and g is gravitational acceleration.Step 3: Recognise that buoyant force is therefore proportional to the mass of displaced liquid.Step 4: Understand that the mass of the body matters only in comparison to the buoyant force when deciding float or sink, not in calculating the buoyancy itself.Step 5: Note that depth of immersion can change the volume displaced, but there is no direct formula linking buoyancy solely to depth.Step 6: Realise that shape influences how much fluid is displaced for a given part of the body, but again buoyancy is fundamentally tied to the mass of displaced fluid.

Verification / Alternative check:
Consider two blocks of different materials but identical volumes placed in the same liquid. Each displaces the same volume of fluid and therefore the same mass of fluid, so they experience the same buoyant force, even if their masses differ. This observation supports the idea that buoyancy depends on displaced fluid, not on the body mass itself. Experiments with floating and sinking objects in water also confirm that what matters is whether the weight of the fluid displaced is enough to balance the weight of the object.

Why Other Options Are Wrong:
The mass of the body alone does not determine the buoyant force; rather it determines whether the body sinks or floats when compared with buoyancy. Depth of immersion does not independently determine buoyancy unless it changes the volume of displaced fluid, and in very deep water the buoyant force is still about the same for the same displacement. The exact shape of the body matters only because it affects how much fluid is displaced for a given part of the body; it is not the primary variable in the expression for buoyancy.

Common Pitfalls:
Students often confuse the rule for floating or sinking with the formula for buoyancy. They may think heavy objects cannot float, forgetting that ships made of steel float because they are shaped to displace enough water. To avoid this confusion, remember that buoyant force is determined by the fluid displaced, not directly by the mass of the body, and use Archimedes principle as your guide.

Final Answer:
Buoyancy depends primarily on the mass (or weight) of the liquid displaced by the body.