Four different objects are completely submerged in a tank of fresh water. The mass of each… — Armed Services Vocational Aptitude Battery (ASVAB)

Four different objects are completely submerged in a tank of fresh water. The mass of each object and the volume of water it displaces are recorded below. Arrange the objects in order of the buoyant force exerted on them by the water, from LEAST buoyant force to GREATEST buoyant force.

1A $3.0 \text{ kg}$ solid iron weight displacing $0.2 \text{ L}$ of water
2A $2.0 \text{ kg}$ solid lead brick displacing $0.5 \text{ L}$ of water
3A $1.0 \text{ kg}$ solid aluminum gear displacing $1.0 \text{ L}$ of water
4A $0.5 \text{ kg}$ wooden block held completely underwater, displacing $2.0 \text{ L}$ of water

Answer

The correct sequence from least to greatest buoyant force is: Iron weight, Lead brick, Aluminum gear, Wooden block.

According to Archimedes' principle, the buoyant force acting on an object is equal to the weight of the fluid it displaces. Because all the objects are in the same fresh water, the buoyant force is directly proportional to the displaced volume. By ordering the displaced volumes from smallest to largest (

0.2 \text{ L}

0.5 \text{ L}

1.0 \text{ L}

2.0 \text{ L}

), we accurately order the buoyant forces from least to greatest.

Step-by-Step Solution

Recall the definition of Archimedes' principle.

The buoyant force acting on a submerged object is equal to the weight of the fluid that the object displaces.

This principle establishes that when objects are submerged in the same fluid, the buoyant force depends entirely on the volume of fluid displaced, not the mass of the objects themselves.

Extract the relevant data for each object.

Iron =

0.2 \text{ L}

, Lead =

0.5 \text{ L}

, Aluminum =

1.0 \text{ L}

, Wood =

2.0 \text{ L}

The mass values provided (

0.5 \text{ kg}

3.0 \text{ kg}

) are distractor information and should be ignored for calculating buoyant force.

Rank the objects based on their displaced volumes from least to greatest.

Iron (

0.2 \text{ L}

) < Lead (

0.5 \text{ L}

) < Aluminum (

1.0 \text{ L}

) < Wood (

2.0 \text{ L}

Since greater displaced volume equals greater buoyant force, this is the final correct order.

Key Concept

According to Archimedes' Principle, the buoyant force on a submerged object depends only on the density of the fluid and the volume of the fluid displaced, completely independent of the object's mass or weight.

Estimated Time:45s

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