Hooke's Law Defines Proportional Limit and Spring Constant

Steps:

• Locate the straight-line portion of the load-extension graph, where extension is proportional to load (Hooke's law: F = kx).
• Identify point Q as the end of this straight line, marking the limit of proportionality where deviation begins.
• Calculate the spring constant k as the gradient (slope) of the straight-line segment.
• Confirm the proportional segment is PR, so k equals the gradient of PR.

Why A is correct:

• Q is the limit of proportionality (end of straight line per Hooke's law), and k equals the gradient of PR (the proportional region, F/x).

Why the others are wrong:

• B: Q is correct limit, but QR gradient is in non-proportional (curved) region, invalid for k.
• C: R is beyond proportionality (in curved region), and PQ gradient is only partial segment, not full proportional k.
• D: R is not the limit (past proportionality), and QR gradient is curved, not for k.

Final answer: A