Young's modulus requires stress-strain relation from load-extension data

Steps:

• Calculate cross-sectional area A = π (d/2)^2, with d = 2.9 × 10^{-3} m, so r = 1.45 × 10^{-3} m, A ≈ 6.6 × 10^{-6} m².
• Young's modulus Y = (F / A) / (ΔL / L) = F L / (A ΔL), where ΔL is extension.
• Graph shows scale reading (assume ΔL) vs. F; slope m = ΔL / F gives Y = L / (A m).
• Not enough information: no graph data for m or numerical L provided.

Why D is correct:

• D matches calculated Y if graph slope and L yield low value (e.g., soft metal or specific setup), per standard formula.

Why the others are wrong:

• A: Overestimates by factor ~250, likely ignores pulley mechanics or miscalculates strain.
• B: Overestimates by ~36, possible area error (e.g., wrong units for diameter).
• C: Overestimates by ~8, perhaps double-counts effective length in pulley setup.

Final answer: D