A head for the linear dimension checking of mechanical pieces including a casing, an arm carrying a feeler for touching a surface of the mechanical piece to be checked, a fulcrum, coupled to the casing and the arm, for enabling displacements of the arm with respect to the casing and a transducer for providing signals depending on the position of the arm with respect to the casing. The head has specific flexibility and modularity features, thanks to the possibility of operating from the exterior for adjusting and replacing various components. The transducer is of the inductive, half-bridge type, with multiple windings. An integral element for the electric connection to a processing unit includes the windings of the transducer, a cable and a connector, and the latter comprises a rapid locking/unlocking device. The ends of the cable are connected between the windings of the transducer and the connector by means of an over-moulding process of a plastic material. A checking apparatus, including at least a gauging or measuring head, includes a stationary structure and at least a support structure for the head, coupled to the stationary structure in an adjustable and removable way.