When a mild steel bar is loaded gradually in tension, the early portion of its stress–strain curve is a straight line. This linear behaviour is described by Hooke's Law, which states that within the elastic limit stress is directly proportional to strain:

σ ∝ ε, or written with the constant of proportionality, σ = E·ε.

• Here E is Young's modulus (modulus of elasticity), the slope of the straight-line region. For mild steel, E ≈ 200 GPa.
• Because the relation is linear, doubling the load doubles both the stress and the strain, and on unloading the bar returns to its original length — the deformation is fully recoverable (elastic).
• This proportionality holds only up to the limit of proportionality (essentially the elastic limit). Beyond it the curve bends over, the material yields, and permanent (plastic) deformation sets in, so σ and ε are no longer proportional.

Therefore the correct relation is Stress ∝ Strain.

Why the other choices are wrong: Stress ∝ (Strain)² and Stress ∝ √(Strain) both describe non-linear (curved) responses, which only occur after yielding — not within the elastic limit. Stress independent of strain would mean a horizontal line (stress unaffected by stretching), which is untrue in the elastic region; it loosely resembles only the flat yield plateau, again outside the elastic range.