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Light does not have mass, but photons are Energy, and E=mc2, so it has relativistic mass (Uh I think! ... I'm not a physicist), but that mass is relative to its velocity so its not what we technically think of as mass...
Light also has momentum, which is how it is able to move something, however I don't conceptually understand how light has momentum despite lacking mass, as mass is a component of momentum.
I have not answered your question at all!
https://en.wikipedia.org/wiki/Mass_in_special_relativity
Mass in special relativity
Mass in special relativity incorporates the general understandings from the laws of motion of special relativity along with its concept of mass–energy equivalence. The word mass is given two meanings in special relativity: one (rest or invariant mass, and its equivalent rest energy) is an invariant quantity which is the same for all observers in all reference frames; the other (relativistic mass or the equivalent total energy of the body) is dependent on the velocity of the observer. The term relativistic mass tends not to be used in particle and nuclear physics and is often avoided by writers on special relativity. They do, however, talk about the (total) energy of a body, which is the equivalent to its relativistic mass, rather than the rest energy equivalent to its rest mass.