The coefficients of thermal expansion of steel and a metal X are respectively 12 ×10⁻⁶ and 2 ×10⁻⁶ per°C. At 40°C, the side of a cube of metal X was measured using a steel vernier callipers. The reading was 100 mm. Assuming that the calibration of the vernier was done at 0°C, then the actual length of the side of the cube at 0°C will be
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Question

The coefficients of thermal expansion of steel and a metal X are respectively 12 ×10⁻⁶ and 2 ×10⁻⁶ per°C. At 40°C, the side of a cube of metal X was measured using a steel vernier callipers. The reading was 100 mm. Assuming that the calibration of the vernier was done at 0°C, then the actual length of the side of the cube at 0°C will be

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G1 Physics · Accepted Answer

Use ΔL=αLΔT, ΔA≈2αAΔT and ΔV≈3αVΔT (or the given cubical coefficient γ). For constrained bodies include the elastic stress needed to cancel free expansion. Evaluating the given data/statements gives > 100 mm. Therefore the correct answer is A.