The governing authorities of municipalities may provide that any person desiring to subdivide a tract of land within the corporate limits shall submit a map and plat of such subdivision, and a correct abstract of title of the land platted, to said governing authorities, to be approved by them before the same shall be filed for record in the land records of the county. Where the municipality has adopted an ordinance so providing, no such map or plat of any such subdivision shall be recorded by the chancery clerk unless same has been approved by said governing authorities. In all cases where a map or plat of the subdivision is submitted to the governing authorities of a municipality, and is by them approved, all streets, roads, alleys and other public ways set forth and shown on said map or plat shall be thereby dedicated to the public use, and shall not be used otherwise unless and until said map or plat is vacated in the manner provided by law, notwithstanding that said streets, roads, alleys or other public ways have not been actually opened for the use of the public. If any easement dedicated pursuant to the provisions of this section for a street, road, alley or other public purpose is determined to be not needed for the public purpose, the easement may be declared abandoned, and ownership of the fee underlying the easement shall revert, regardless of the date of dedication, to the adjoining property owner or owners at the time of abandonment. Ownership of the easement shall extend to the centerline of said abandoned street, road or public way. Such abandonment and reversion shall not affect any private easements which might exist.