Question

Why ordinary moving coil galvanometer cannot be used to measure ac?

Answer 1

A galvanometer is a moving coil instrument, where the magnetic force applied by the current is opposed by a (hair) spring, so that the deflection is proportional to the current.

An AC current would make the force oscilate, but the inertia of the moving element would probably make this invisible. They are intended for DC only.

That said, any DC instrument can be fed with rectified AC to get a deflection, and the rectifier introduces relatively well known errors (the forward volts drop and the form factor) which can be accounted for in drawing an AC scale.