Question

Object 1 and Object 2 float in beakers of water as shown below. Which of the following statements about the objects must be true?

Option 1: The density of Object 1 is less than the density of Object 2.
Option 2: Object 1 is less buoyant than Object 2.
Option 3: Object 1 has a greater mass than Object 2.
Option 4: The volume of Object 2 is greater than the volume of Object 1.

Answer 1

The average density of an object in relation to water determines its buoyancy due to Archimedes' principle. Therefore, if Object 1 floats higher than Object 2, it means Object 1 has a lower density than Object 2.

Step-by-step explanation:

When two objects float in beakers of water, the average density of the objects relative to the water determines whether they sink or float, according to Archimedes' principle. If the average density of an object is less than the density of water, it will float because the buoyant force, which equals the weight of the water displaced, will be greater than the weight of the object. Given two floating objects, if one object is floating higher than the other, it suggests that it has a lower density compared to the other. Therefore, Option 1 must be true: The density of Object 1 is less than the density of Object 2. However, we cannot determine the relative masses or volumes of the objects purely based on their floating.