(a) The assessor of the town of North Providence, on or before June 1 of each year, shall make a full and fair cash valuation of all the estate, real and personal, including motor vehicles and trailers, subject to taxation, and determine the assessed valuation of each property class.
(b) The assessor has the authority to apply different rates of taxation against class one, class two, class three and class four property to determine the tax due and payable on the property; provided, that the rate of taxation is uniform within each class.