For each of the given scenarios and based on the volume, mass, and density of the spheres, the water level is given as follows:
Scenario 1: The water level will rise; r
Scenario 2: The water level may rise or fall; r or f
Scenario 3: The water level will fall; f
<h3>What is the relationship between volume, density, and mass of the objects?</h3>
The density, volume and mass of an object are related by the formula below:
The rise in the level of fluid when an object is placed in that fluid depends on the weight, volume and density of that object.
This is given by Archimedes' principle which states that the upthrust acting on a body immersed fully or partially in a fluid, is equal to the weight of the fluid displaced.
Based on the above, the water level in each of the scenarios is described thus:
Scenario 1: The new sphere has a radius of r < r0 and a mass of m > m0.
The new has a smaller volume and a greater mass and density. The water level will rise.
Scenario 2: The new sphere has a mass of m > m0 and a density of ρ < ρ0.
The new sphere has a greater volume and will float. Therefore, the water level may rise or fall.
Scenario 3: The new sphere has a density of ρ < ρ0 and a radius of r > r0.
The new sphere has a greater volume but less mass. Therefore, the water level will fall.
In conclusion, the rise or fall of the water level in the container depends on the volume, mass, and density of the spheres.
Learn more about Archimedes principle at: brainly.com/question/775316
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