Deformation of Solids: Question 8
Syllabus 6.2
A metal wire is stretched by a steadily increasing force until it has been deformed well beyond its elastic limit. The force is then removed completely.
Which statement correctly describes what happens to the wire once the force has been removed?
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Worked solution
Recalling elastic and plastic deformation
A material deformed only as far as its elastic limit returns exactly to its original dimensions once the deforming force is removed (this is elastic deformation. Beyond the elastic limit, some of the deformation becomes permanent, even after the force is fully removed) this is plastic deformation.
The limit of proportionality is a different (usually earlier) point, beyond which is no longer directly proportional to , but the deformation can still be fully elastic between the limit of proportionality and the elastic limit.
Applying this to the wire
The question states the wire is stretched well beyond its elastic limit. Since the elastic limit has been exceeded, the deformation is no longer fully reversible: once the force is removed, some permanent extension remains, and the wire does not return to its original length.
Why the other options are wrong
- A: incorrectly assumes all deformation is reversible; this is only true up to the elastic limit.
- B: confuses the limit of proportionality with the elastic limit. A wire stretched beyond the limit of proportionality but still within the elastic limit does return to its original length, but that is not what determines full recovery here.
- D: there is no physical mechanism by which the plastic (permanent) extension of a wire disappears over time on its own; the permanent deformation remains indefinitely.
Final answer
- The wire does not return to its original length, because it has undergone plastic deformation, option C.