All resolutions and motions (i) that create any liability against a city, (ii) that provide for the expenditure or appropriation of its money, or (iii) to sell any city or school property, and all ordinances, passed by the city council shall be deposited with the city clerk. Except as provided in Articles 4 and 5 of this Code, if the mayor approves an ordinance or resolution, the mayor shall sign it. Those ordinances, resolutions, and motions which the mayor disapproves shall be returned to the city council, with the mayor’s written objections, at the next regular meeting of the city council occurring not less than 5 days after their passage. The mayor may disapprove of any one or more sums appropriated in any ordinance, resolution, or motion making an appropriation, and, if so, the remainder shall be effective. However, the mayor may disapprove entirely of an ordinance, resolution, or motion making an appropriation. If the mayor fails to return any ordinance or any specified resolution or motion with his written objections within the designated time, it shall become effective despite the absence of the mayor’s signature.