can moving coil galvanometer be used to detect an ac circuit?

No , its simply cant be used because due to continuous shifting of phases of current (reversal of direction of current after a certain period of time ) , it will continue to rotate the coil inside the galvanometer to and fro and as such no tortion could be developed in the quartz wire. If something like this is  done ,the needle of the galvanometer will simply continue to move to and fro about its mean position until the quatz wire breaks (if the frequency is small) . If the frequncy of the ac current is large, nothing is observable and the needle will stay in its position.