No, two homogeneous bodies of the same volume do have not the same mass.
No, two objects don't need to have same volume to have the same mass because the density of the objects they are made up of can be different from one another. Mass and volume are independent, two objects with the same volume can have different amounts of masses. So that's why the objects can have different densities. Density is defined as the mass of the substance divided by its volume.
Density = mass /volume
Mass is defined as the amount of matter that is present in an object, while on the other hand, volume is the space occupied by an object. For example, a bowling ball and a basketball have the same volume but the bowling ball has more mass.
So we can conclude that two homogeneous bodies of the same volume do have not the same mass because of the difference in their volume.
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