Section 4. Every ordinance, order, resolution or vote requiring the concurrence of the board of aldermen and of the common council, except the question of a convention of the two branches or of the election of an officer, shall be presented to the mayor. If he approves it, he shall sign it; if he disapproves it, he shall return it, with his written objections, to the branch wherein it originated, which shall enter such objections at large on its records and again consider it; and if two thirds of the members present and voting pass it, notwithstanding such objections, it shall, if not originally requiring concurrent action, be in force; but if originally requiring concurrent action, it shall be sent, with the objections of the mayor, to the other branch, where it shall be again considered, and if passed by two thirds of the members present and voting, it shall be in force; but in all cases the vote shall be by yeas and nays. Such ordinance, order, resolution or vote shall be in force if not returned by the mayor within ten days after it has been presented to him. This section shall not apply to budgets submitted under section thirty-two of chapter forty-four, or to appropriations by a city council under section thirty-three of said chapter.