What is the reason that moving iron instrument can measure both AC and DC but moving coil instrument can't?
A moving coil meter uses a magnet and this naturally means that the needle moves clockwise for a positive current and anti-clockwise for negative current. The average effect (due to mechanism inertia) and an applied AC frequency of 50 or 60 Hz usually nothing i.e. zero perceptible movement.

A moving iron meter will attract an iron armature irrespective of the direction of the current hence, it will measure AC and usually will measure RMS AC quantities.