neither of these things exist and therefore there is no meaningful answer to this question.
Actually, there is an answer. something can only be stationary as relative to something else. therefore the irresistible force would transfer all of its momentum to the object which would then travel through space along with anything attached to it. As an example, If we took a big steel board and attached it onto the moon with a (imaginary) perfect mechanism than that would constitute or unmovable object. then we launch a giant baseball at it (our "irresistible force). The baseball would transfer all (or some) of it's kinetic energy to the board and the moon would start moving in the same direction as the baseball but with added spin, since the force on the moon is only coming from the side with the board on it.
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neither of these things exist and therefore there is no meaningful answer to this question.
Actually, there is an answer. something can only be stationary as relative to something else. therefore the irresistible force would transfer all of its momentum to the object which would then travel through space along with anything attached to it. As an example, If we took a big steel board and attached it onto the moon with a (imaginary) perfect mechanism than that would constitute or unmovable object. then we launch a giant baseball at it (our "irresistible force). The baseball would transfer all (or some) of it's kinetic energy to the board and the moon would start moving in the same direction as the baseball but with added spin, since the force on the moon is only coming from the side with the board on it.