Identify the correct statement.

Asked in SSC JE 29/01/2018 (Morning)

Detailed Explanation

On the stress–strain curve of mild steel, the first part is a straight line. Just after it there is a short region that is still elastic but no longer straight.

Why “Hooke's law is valid up to the limit of proportionality” Is Correct

Hooke's law (stress ∝ strain) holds only on the straight part, i.e. up to the limit of proportionality. The elastic limit is slightly higher: up to it the material still recovers fully, but the curve is no longer straight. So (c) is the strict answer.

Note: in the revised key the commission did not accept a single option, because many books treat the limit of proportionality and the elastic limit as practically the same point for mild steel.

Stress–strain curve of mild steel in tension. O–A: straight line, Hooke's law holds up to the limit of proportionality A. B: elastic limit. C and D: upper and lower yield points. D–E: yielding at nearly constant stress. E–F: strain hardening up to the ultimate stress F. G: fracture.

Why the Other Options Are Wrong

A. Hooke's law is valid up to the elastic limit: The elastic limit is a little beyond the straight-line range; many books treat it as equal, hence the dispute.
B. Hooke's law is valid up to the yield point: Beyond the elastic limit, permanent set occurs; the yield point is further still.
D. Hooke's law is valid up to the last point: After yield the curve is strongly non-linear.

Key Point

Limit of proportionality (Hooke's law) ≤ elastic limit < yield point.

Key Concepts for Students

E is the slope of the straight part.
Permanent set remains after unloading beyond the elastic limit.
Brittle materials have no clear yield point.

Practice more: this is question 23 in Stress and Strain MCQs – Part 2. Try the whole set and check every answer instantly.