Answer :
Final answer:
The accessory used to support long thin shafts on a lathe carriage is called a steady rest. It provides support to prevent deflection and vibration during machining. It is distinct from other components like follower rests or collets.
Explanation:
The accessory attached to the carriage on a lathe that is used to support long thin shafts is known as a steady rest. The steady rest, also called a steady or center rest, is a fixed bearing that sits on the lathe bed and provides support to long workpieces to prevent deflection, bending, and vibration during machining operations.
It is not to be confused with a follower rest, which moves with the carriage, or with collets, faceplates, lathe centers, and lathe dogs, which also serve to hold or drive workpieces but don't provide the same kind of support for long, slender shafts.