Final answer:
The mass of the bags must be different because weight is influenced by the local force of gravity, which is stronger on Jupiter than on Earth. Thus, for the bags to have the same weight, the mass of the sawdust bag on Jupiter must be lower than the mass of the sugar bag on Earth.
Step-by-step explanation:
The apparent weight of an object is the force exerted on it due to gravity. Although two bags - one of sugar on Earth and another of sawdust on Jupiter - may have the same weight, their masses must differ because the force of gravity on Jupiter is much stronger than on Earth. Gravity is the key factor that causes weight to vary depending on the location, despite mass being an intrinsic property of the object and remaining constant across different environments.
When we say the bags weigh the same, we are observing that the gravitational forces acting on them are equal. However, knowing that Earth's gravity is weaker than Jupiter's, we can deduce that the bag of sugar on Earth has more mass to compensate for the weaker gravitational pull. Conversely, the sawdust on Jupiter can have less mass and still exert the same weight because of Jupiter's stronger gravity.
To summarize, if the weight of two objects is the same but they are on planets with different gravitational strengths, then the mass of the objects must be different. The object on the planet with the stronger gravity (Jupiter, in this case) will have a smaller mass than the object on the planet with weaker gravity (Earth).