The relation between gravitational mass, inertial mass, and velocity

This work concerns a ‘‘thought experiment’’ using a balance whose arm length can be varied in order to prove that, within the scope of the special theory of relativity, both inertial mass and gravitational mass of a moving body obey the relationship m=m₀/(1−v²/c²)^1/2. Therefore, if the inertial mass of a body and its gravitational mass are strictly equal at rest, then they are still equal when the body moves at high velocity. The argument extends Einstein’s principle of equivalence to special relativity.