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 If you stick to an inertial frame, then all you have is the 'accelerating force' on mass A. No other forces involved. (There will, of course, be the 'reaction force' on mass B, but that's a force on B not A.)
 Quote by Studiot If A is the bar and B is one of the masses that is exactly what I said originally and subsequently.
If so, then how do you explain this statement of yours:
 Quote by Studiot Newton's third law states that to every action there is always an equal and opposite reaction. A force applied to a mass with the purpose of accelerating it is referred to as the accelerating force. Immediately this force is applied, an equal and opposite internal force, known as the inertial force, is produced in the mass and this force makes the mass resist any change of motion.
That sure sounds like the two 'forces' being discussed act on the same mass, and thus cannot be Newton's third law pairs.