For a mild steel column with both ends hinged (pinned), select the standard Rankine's constant (a) used in the Rankine–Gordon buckling formula. Choose the value typically adopted in design handbooks.

Introduction:
The Rankine–Gordon formula blends Euler buckling and crushing to predict column strength. It employs a material constant a (Rankine's constant) that depends primarily on material type, not directly on end conditions.

Given Data / Assumptions:

• Material: mild steel.
• Empirical constant a required for Rankine equation.

Concept / Approach:
A typical form is: P = sigma_c * A / (1 + a * (L_e / r)^2). For mild steel, standard references adopt a ≈ 1/7500; for cast iron, a ≈ 1/1600 to 1/9000 depending on source and grade. The choice 1/7500 is widely used for mild steel in exams and handbooks.

Step-by-Step Solution:
1) Identify material: mild steel.2) Recall standard a values from design data.3) Select a = 1/7500.

Verification / Alternative check:
Cross-check with common data books where mild steel is tabulated with a ≈ 1/7500.

Why Other Options Are Wrong:
1/750: excessively large; would under-predict strength.

1/1600 and 1/9000: values often associated with cast iron ranges; not the usual choice for mild steel.

Common Pitfalls:
Mixing a for different materials or confusing a with end-condition factor K (which affects L_e).

Final Answer:
1/7500