Does the buoyant force change in different fluids?

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The buoyant force acting on an object is determined by the weight of the fluid displaced, which varies between different fluids. In the case of two identical objects floating, one in water and the other in saltwater, the buoyant force is equal to the weight of the displaced fluid. Since saltwater is denser than freshwater, the object in saltwater displaces less fluid and floats higher, but the buoyant force remains equal to the weight of the object in both cases. If the object were fully immersed, the buoyant forces would differ due to the varying densities of the fluids. Thus, while the weight of the object does not change, the buoyant force can vary depending on the fluid's density.
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Given two objects of identical density and weight, one is floating on water and the other is floating on saltwater. Is the magnitude of buoyant force acting on the object the same in the two situations? From my thinking, it seems that the weight of the object in the the two situations should not change and so the buoyant force should not change as well (Archimedes principle). Correct me if I'm wrong in that thinking.

Thanks
 
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If both objects are floating in equilibrium, the upwards force on each object (buoyant force) must be equal to the downwards force (weight), so you are correct.

The buoyant force is equal to the weight of the amount of fluid displaced, so the object floating on saltwater will displace less fluid and therefore float higher than the object floating on pure water.
 
However, if the object was fully immersed in water, then the bouyant force WOULD be different.
 
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