Work done equals area under force-extension graph

Steps:

• Work done by a variable force is the integral of force with respect to displacement.
• The force-extension graph plots force (y-axis) against extension (x-axis).
• The area under this curve represents ∫F dx, which is the work done.
• For a spring, this work stores as elastic potential energy.

Why A is correct:

• By definition, work done W = ∫F dx from x=0 to final extension, matching the area under the graph.

Why the others are wrong:

• B: Gradient is the spring constant k (F = kx), not work.
• C: Reciprocal of gradient is 1/k, measuring spring softness, not work.
• D: No factor of two; work is exactly the area, not doubled.

Final answer: A