Vehicles subject to registration under the provisions of this chapter shall be placed in the following classes for the purpose of registration:

Class A. Motor vehicles of passenger type and trucks with a gross weight of ten thousand pounds or less;

Class B. Motor vehicles designated as trucks with a gross weight of more than ten thousand pounds, truck tractors or road tractors;

Class C. All trailers and semitrailers, except house trailers and trailers or semitrailers designed to be drawn by Class A motor vehicles and having a gross weight of less than two thousand pounds;

Class G. Motorcycles and parking enforcement vehicles;

Class H. Motor vehicles operated regularly for the transportation of persons for compensation under a certificate of convenience and necessity or contract carrier permit issued by the Public Service Commission;

Class J. Motor vehicles operated for transportation of persons for compensation by common carriers, not running over a regular route or between fixed termini;

Class M. Mobile equipment as defined in subdivision (oo), section one, article one of this chapter;

Class R. House trailers;

Class T. Trailers or semitrailers of a type designed to be drawn by Class A vehicles and having a gross weight of less than two thousand pounds; and

Class X. Motor vehicles designated as trucks having a minimum gross weight of more than eight thousand pounds and a maximum gross weight of eighty thousand pounds, used exclusively in the conduct of a farming business, engaged in the production of agricultural products by means of: (a) The planting, cultivation and harvesting of agricultural, horticultural, vegetable or other products of the soil; or (b) the raising, feeding and care of livestock, poultry, bees and dairy cattle. A farm truck may be used only for the transportation of agricultural products produced by the owner of the truck, for the transportation of agricultural supplies used in the production or for private passenger use.