A resistance strain gauge has gauge factor G = 2 mounted on a specimen under stress of 1050 kg/cm². If the gauge resistance is 1000 Ω, estimate the change in resistance ΔR (assume steel with E ≈ 2 × 10^6 kg/cm²).

Introduction / Context:
Strain gauges convert mechanical strain into a resistance change. The core relation is ΔR/R = G * ε, where ε is axial strain and G is the gauge factor. To get ε from stress σ, Hooke's law ε = σ / E is used for linear elastic behavior.

Given Data / Assumptions:

• Gauge factor G = 2.
• Stress σ = 1050 kg/cm².
• Gauge resistance R = 1000 Ω.
• Assume material modulus E ≈ 2 × 10^6 kg/cm² (typical steel order of magnitude).

Concept / Approach:
Compute strain ε from σ and E, then apply ΔR = R * G * ε. This is the standard small-strain, linear-elastic estimation widely used in experimental stress analysis.

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