Two bars, same size and tensile force: If unit elongation of material A : material B = 2 : 5, what is the ratio of their moduli of elasticity E_A : E_B?

Introduction / Context:
Axial deformation under the same load relates inversely to the modulus of elasticity when geometry is the same. This question reinforces the proportionality between elongation and 1/E for bars of identical dimensions under identical forces.

Given Data / Assumptions:

• Two bars have the same length L and cross-sectional area A.
• Same tensile force P acts on both bars.
• Unit elongation (strain) ratio A:B = 2:5.
• Linear elastic behavior: delta = P * L / (A * E).

Concept / Approach:
For equal P, L, and A, the elongation (and strain) is inversely proportional to E. Therefore, if strain_A : strain_B = 2 : 5, then E_A : E_B = 5 : 2.

Step-by-Step Solution:

Verification / Alternative check:
Pick numbers: if E_A = 50 and E_B = 20 (arbitrary units), then delta_A ∝ 1/50 and delta_B ∝ 1/20, giving a ratio 0.02 : 0.05 = 2 : 5, confirming.

Why Other Options Are Wrong:
They either invert or distort the correct inverse relationship; 1:1 would imply equal elongations, which contradicts the data.

Common Pitfalls:
Forgetting to invert the ratio; confusing modulus with strength; assuming larger E gives larger elongation (it is the opposite).

Final Answer:
5 : 2