A head for the linear dimension checking of mechanical pieces including a casing, an arm carrying a feeler for touching the mechanical piece to be checked, a fulcrum 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. Various components of the head can be adjusted and/or replaced from the exterior of the casing. 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. 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.