GATE AG 2007 • Q36 MCQ • 1 Mark

Section 2: Farm Machinery

Machine Design

Subtopic: Measurement of force, stress, torque, speed, displacement and acceleration on machine elements – shafts, couplings, keys, bearings and knuckle joints

Question Statement:

A strain gauge of 120 Ω nominal resistance and 2.1 gauge factor is mounted on a tensile steel member. The longitudinal axis of the strain gauge is along the length of the member. Young's modulus of steel is 2.1×10¹¹ Pa. The change in resistance of the gauge is 0.08064 Ω. The stress experienced by the steel member is

Options:

  • (A) 67.2 × 10⁶ Pa
  • (B) 141.1 × 10⁶ Pa
  • (C) 268.8 × 10⁶ Pa
  • (D) 296.4 × 10⁶ Pa

Official Answer Key:

A

Step-by-Step Solution & Explanation

Gauge factor: GF = (ΔR/R)/ε ⟹ ε = (ΔR/R)/GF = (0.08064/120)/2.1 = 6.72×10⁻⁴/2.1 = 3.2×10⁻⁴. Stress = E·ε = 2.1×10¹¹ × 3.2×10⁻⁴ = 67.2×10⁶ Pa.

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