Section 16. In towns which have a population of more than five thousand and which have not already satisfied the provisions of the preceding section or corresponding provisions of earlier laws, upon petition to the selectmen by ten per cent of the voters filed fifteen days before the day of the annual election of town officers, the following question shall be submitted to the town at the next annual meeting or shall be placed on the official ballot, if any, at the next town election: ''Shall section fifteen of chapter forty-five of the General Laws, requiring certain towns to provide public playgrounds, be accepted by this town?'' Said section shall take effect in any town to which it applies upon its acceptance by a majority of the voters voting as aforesaid.