Elastic potential energy from force-extension graph

Steps:

• Identify the graph as force (F) versus extension (x), where area under curve represents work done by force.
• Recall that for elastic deformation, work done stores as elastic potential energy (½kx² or integral F dx).
• At point S, area under graph up to S gives total elastic PE if within elastic limit.
• Verify other options contradict standard wire behavior: proportionality ends at straight-line limit, plastic deformation follows.

Why B is correct:

• Elastic potential energy equals work done by applied force, which is the area under the F-x graph (from definition of work as ∫F dx).

Why the others are wrong:

• A: Limit of proportionality is end of straight line, likely before R if R follows deviation.
• C: Between Q (likely yield point) and P (max force), plastic deformation occurs as extension continues without full recovery.
• D: Hooke's law (F ∝ x) holds only up to proportionality limit, not beyond into R-Q region.

Final answer: B