In a centrifugal casting method, the correct answer is option 'A': no core is used. This means that in this casting process, a core is not necessary to create the desired final shape of the casting.

Centrifugal casting is a technique used to manufacture cylindrical or symmetrical shaped objects such as pipes, tubes, and rings. It involves the use of centrifugal force to distribute molten metal into a mold cavity. The molten metal is poured into a rotating mold, and due to the centrifugal force, it is forced against the inner surface of the mold cavity, creating the desired shape.

Now, let's examine why a core is not used in centrifugal casting:

1. Definition of a core: In casting processes, a core is a pre-formed sand or metal insert that is positioned within the mold to create hollow areas, internal passages, or complex shapes in the final casting.

2. Purpose of a core: Cores are used when the desired final shape of the casting includes internal features that cannot be achieved solely by the outer mold cavity. Cores provide a means to create these internal features, such as holes, recesses, or undercuts.

3. Centrifugal casting process: In centrifugal casting, the molten metal is poured into a rotating mold, and the centrifugal force distributes the metal evenly against the mold cavity walls. As the mold rotates, the molten metal solidifies, forming the desired shape.

4. No need for internal features: The centrifugal casting process is primarily used for producing simple, cylindrical shapes without complex internal features. The rotation of the mold ensures that the molten metal spreads evenly along the inner surface of the mold, resulting in a uniform wall thickness throughout the casting.

5. Simplicity and cost-effectiveness: By eliminating the need for a core, the centrifugal casting process becomes simpler and more cost-effective. The absence of a core reduces the complexity of the casting operation and eliminates the need for additional materials and labor to create and position the core.

In conclusion, in the centrifugal casting method, no core is used because the process is primarily used to produce simple cylindrical shapes without complex internal features. The rotation of the mold ensures that the molten metal spreads evenly along the inner surface of the mold, eliminating the need for a core to create these internal features.