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Difficulty: MediumBuoyancy and Archimedes' Principle

Two solid machine components, Component X and Component Y, have the exact same volume but are cast from different metals. Component X weighs 15 N15 \text{ N} in air, and Component Y weighs 45 N45 \text{ N} in air.

Both components are separately lowered into identical displacement tanks filled to the brim with water. When Component X is completely submerged, exactly 5 N5 \text{ N} of water spills out of the tank. When Component Y is completely submerged, what is the weight of the water that spills out?

  1. 5 N5 \text{ N}Answer
  2. B
    15 N15 \text{ N}
  3. C
    40 N40 \text{ N}
  4. D
    45 N45 \text{ N}

Answer

The weight of the water that spills out is 5 N5 \text{ N}.
The correct answer is 5 N5 \text{ N}. When an object is fully submerged in a fluid, it displaces a volume of fluid equal to its own volume. According to Archimedes' Principle, the buoyant force acting on the object is equal to the weight of this displaced fluid. Because Component Y has the exact same volume as Component X, it must displace the exact same amount of water, meaning the weight of the overflowing water remains 5 N5 \text{ N}. The object's weight in air does not affect how much fluid it displaces once it is completely submerged.

Step-by-Step Solution

1
Identify the relationship between the two components.
Both Component X and Component Y share the exact same volume, despite having different weights in air.
The physical volume of an object dictates how much fluid it can displace when fully submerged.
2
Apply Archimedes' principle of displacement.
Because both components have identical volumes, completely submerging either one will displace the exact same volume of water.
A fully submerged object always displaces a volume of fluid equal to its own total volume, regardless of its density or mass.
3
Determine the weight of the displaced water for Component Y.
Since Component X displaced 5 N5 \text{ N} of water, Component Y must also displace 5 N5 \text{ N} of water.
Equal volumes of the same fluid (water) will naturally have the same weight.

Key Concept

Buoyancy and Archimedes' Principle
Estimated Time:1m 0s
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Topics

Buoyancy and Archimedes' Principle

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