Area under force-extension graph equals work done

Steps:

• Identify graph axes: y-axis is force (F), x-axis is extension (Δx, a displacement).
• Recall that work done (W) by a force is the integral of F d(Δx), or area under the F-Δx curve.
• Confirm extension represents linear displacement for the wire.
• Conclude the area quantifies total work done on the wire during extension.

Why D is correct:

• Work done on the wire is defined as W = ∫F d(Δx), directly given by the area under the force-extension graph.

Why the others are wrong:

• A: Power is work per unit time (P = W/t); no time axis present.
• B: Time taken requires a time axis, absent from the graph.
• C: Temperature increase relates to internal energy from work, but the area measures mechanical work, not thermal change.

Final answer: D