Error propagation amplifies diameter's uncertainty due to squared term

Steps:

• Young's modulus formula: E = (4 F L) / (π d² x), where cross-sectional area A = π d² / 4.
• Relative uncertainty: δE/E ≈ δF/F + δL/L + δx/x + 2 (δd/d), from partial derivatives.
• The coefficient 2 for δd/d doubles its relative error compared to linear terms.
• With typical equal percentage errors in measurements, diameter's term dominates uncertainty in E.

Why B is correct:

• Diameter d is squared in the denominator (A ∝ d²), so error propagation gives 2(δd/d), amplifying its impact per the standard uncertainty formula.

Why the others are wrong:

• A: Length L is linear in numerator, contributing only δL/L.
• C: Force F is linear in numerator, contributing only δF/F.
• D: Extension x is linear in denominator, contributing only δx/x.

Final answer: B