Abstract: The Eötvös experiment on the verification of equivalence between inertial mass and gravitational mass of a body is famous for its accuracy. A question is, however, can these experimental results be applied to the case of a physical space in general relativity, where the space coordinates could be arbitrary? It is pointed out that it can be validly applied because it has been proven that Einstein's equivalence principle for a physical space must have a frame of reference with the Euclidean-like structure. Will claimed further that such an overall accuracy can be translated into an accuracy of the equivalence between inertial mass and each type of energy. It is shown that, according to general relativity, such a claim is incorrect. The root of this problem is due to an inadequate understanding of special relativity that produced the famous equation $E=mc^2$, which must be understood in terms of energy conservation. Concurrently, it is pointed out that this error is a problem in Will's book, `Theory and Experiment in Gravitational Physics'.

Key words: Einstein's equivalence principle, Einstein--Minkowski condition, Euclidean-like structure, Eötvös experiment, weak equivalence principle, $E=mc^2$