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Question

An object is fully submerged in a fluid. Which of the following is directly proportional to the upthrust experienced by the object?

SUBHANI · Accepted Answer

## CORE INFORMATION
✓ **Answer**: D
## CONCEPT FRAMEWORK
	**Primary Concept**: Archimedes' principle
	**Related Topics**: Buoyancy, fluid pressure, density
	**Prerequisites**: Understanding of density, volume, and pressure.
## SOLUTION PATHWAY
**Given Information**:
		An object is fully submerged in a fluid.
		We need to find the factor directly proportional to the upthrust (buoyant force).
**Method & Steps**:
	1. Recall Archimedes' principle: The upthrust on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
		Reasoning: The upthrust is a consequence of the pressure difference between the top and bottom surfaces of the submerged object.
		Formula/Rule: $F_b = ho_f V_f g$, where $F_b$ is the buoyant force (upthrust), $ho_f$ is the density of the fluid, $V_f$ is the volume of the fluid displaced, and $g$ is the acceleration due to gravity.
	2. Since the object is fully submerged, the volume of the fluid displaced ($V_f$) is equal to the volume of the object submerged ($V_{obj}$).
		Working: $F_b = ho_f V_{obj} g$
		Key Point: The upthrust depends on the density of the fluid and the volume of the object submerged, but not on the object's mass, density, or surface area.
	3. From the formula, we see that the upthrust ($F_b$) is directly proportional to the volume of the object submerged ($V_{obj}$).
		Result: The volume of the object submerged is directly proportional to the upthrust.
		Verification: If we double the volume of the submerged object, we double the volume of fluid displaced, thus doubling the upthrust.
## OPTION ANALYSIS
A :x: Mass of the object affects the weight of the object, not directly the upthrust.
B :x: Density of the object affects the weight of the object, not directly the upthrust.
 C :x: Surface area of the object does not directly influence the upthrust. The upthrust is determined by the volume of fluid displaced.
D ✓: Volume of the object submerged directly determines the volume of fluid displaced, and hence directly affects the upthrust according to Archimedes' principle.
## LEARNING AIDS
	**Common Mistakes**:
		1.Confusing upthrust with weight: Upthrust is the upward force exerted by the fluid, while weight is the force due to gravity.
			How to avoid: Clearly distinguish between the forces acting on the object.
		2.Ignoring the density of the fluid: The upthrust depends on both the volume of fluid displaced and the density of the fluid.
			How to avoid: Remember and use the correct formula for Archimedes' principle.
	**Quick Tips**:
		1.Visualize the volume of water displaced – that's directly related to the upthrust.
		2.Remember Archimedes' principle:  Upthrust = weight of fluid displaced.

SUBHANI · Answer

Mass of the object

SUBHANI · Answer

Density of the object

SUBHANI · Answer

Surface area of the object

SUBHANI · Answer

The correct Option is "Volume of the object submerged"

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