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).

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Solve this multiple-choice question and choose the correct option.

Accepted Answer

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. Step-by-Step Solution: ε = σ / E = 1050 / (2 × 10^6) = 5.25 × 10^-4ΔR/R = G * ε = 2 * 5.25 × 10^-4 = 1.05 × 10^-3ΔR = R * (ΔR/R) = 1000 × 1.05 × 10^-3 ≈ 1.05 Ω ≈ 1 Ω Verification / Alternative check: Using E = 2.1 × 10^6 kg/cm² gives ΔR ≈ 1.0 Ω; either way the closest option is 1 Ω. Why Other Options Are Wrong: 2–4 Ω would require roughly double to quadruple the computed strain; 0.5 Ω is about half the computed change. Common Pitfalls: Forgetting to convert stress to strain using E; misapplying gauge factor relation. Final Answer: 1 Ω

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).

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