Final answer:
Objects of the same size and shape, but different mass, will displace the same amount of water.
Step-by-step explanation:
According to Archimedes' principle, an object will displace a volume of water equal to its own volume when it is submerged in water. Therefore, objects of the same size and shape but different mass will indeed displace the same amount of water, meaning they will have the same volume.
For example, if we have two objects, one made of wood and the other made of brass, both having the same size and shape, when placed in a fish tank filled with water, both objects will displace the same amount of water. The block of wood will float, and the cube of brass will sink because the block of wood has a much greater volume due to its lower density.
It's important to note that while the mass and volume of the objects may be different, the density will vary. Density is the ratio of an object's mass to its volume, and it's what determines whether an object will sink or float in water.