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Difficulty: HardBuoyancy and Archimedes' Principle

An overflow container is filled to the brim with a specialized drilling mud that weighs 15 N15 \text{ N} per liter. A solid geological core sample weighing 75 N75 \text{ N} in the air is completely submerged in the mud, causing exactly 22 liters of mud to spill into a measuring basin. Based on Archimedes' principle, what is the apparent weight of the core sample while it is fully suspended in the mud?

  1. 45 N45 \text{ N}Answer
  2. B
    30 N30 \text{ N}
  3. C
    60 N60 \text{ N}
  4. D
    105 N105 \text{ N}

Answer

The apparent weight of the core sample is 45 N45 \text{ N}.
Archimedes' principle dictates that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. Because the core sample displaces 22 liters of mud (which weighs 15 N15 \text{ N} per liter), the upward buoyant force is 30 N30 \text{ N}. The apparent weight is the actual downward weight (75 N75 \text{ N}) minus this upward buoyant force (30 N30 \text{ N}), resulting in a net apparent weight of 45 N45 \text{ N}.

Step-by-Step Solution

1
Calculate the weight of the displaced drilling mud.
2 liters×15 N/liter=30 N2 \text{ liters} \times 15 \text{ N/liter} = 30 \text{ N}
According to Archimedes' principle, the upward buoyant force acting on a submerged object is exactly equal to the weight of the fluid it displaces.
2
Calculate the apparent weight of the submerged core sample.
75 N−30 N=45 N75 \text{ N} - 30 \text{ N} = 45 \text{ N}
The apparent weight is determined by subtracting the upward buoyant force from the actual downward weight of the object.

Key Concept

Apparent weight and Archimedes' principle
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Topics

Buoyancy and Archimedes' Principle

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