What is the mass of the particle as observed by O and O'?

In the context of physics, particularly in relativistic mechanics, the mass of a particle can be described in two ways: rest mass (often denoted as m0) and relativistic mass (denoted as m). The rest mass, m0, is the mass of the particle as measured in the particle's own rest frame, where it is not moving relative to the observer. The relativistic mass, m, is the mass of the particle as measured by an observer who sees the particle moving relative to themselves.

When discussing the mass of a particle as observed by two different observers, O and O', you'll find that the rest mass (m0) is invariant, meaning it does not change regardless of the relative motion between observers. On the other hand, the relativistic mass (m) increases with the speed of the particle as perceived by the other observer, according to the effects of special relativity.

Thus, one observer will measure the particle's rest mass m0 (when they are at rest relative to it), while the other observer will measure the relativistic mass m (when they see the particle moving). Therefore, it is correct to say that the masses observed by O and O' are represented as m and m0, reflecting