Question

Bucket $A$ contains only water; an identical bucket $B$ contains water, but also contains a solid object in the water. Consider the following four situations. Which bucket weighs more?

Answer 1

Buoyant force is the weight of the water displaced by the object. This buoyant force's reaction pair would act on the bucket's water downwards, adding to the bucket's weight.

When the buckets have same water level with object floating in B, there would have been no change due to buoyant force since water of amount with same weight as that of buoyant force is missing in order to maintain same level. Hence both the buckets would weight the same.

When object floats in B with buckets having same volume, the implicit weight of the water is same in both buckets, but the buoyant force is added extra. Hence the Bucket B weighs more.

In the case of object sinking completely with same water level in the buckets, the weight of the object adds to the weight of the bucket instead of a buoyant force. Hence it weighs more than the other bucket.

An argument similar to the statement B's support would be used, but instead of buoyant force we would have the weight of the object added.