A metallic bar of Young's modulus 0.5 × 10¹¹ N m⁻² and coefficient of linear thermal expansion 10⁻⁵ °C⁻¹, length 1 m and area of cross-section 10⁻³ m² is heated from 0°C to 100°C without expansion or bending. The compressive force developed in it is:
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Question

A metallic bar of Young's modulus 0.5 × 10¹¹ N m⁻² and coefficient of linear thermal expansion 10⁻⁵ °C⁻¹, length 1 m and area of cross-section 10⁻³ m² is heated from 0°C to 100°C without expansion or bending. The compressive force developed in it is:

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G1 Physics · Accepted Answer

Step 1: A free bar would develop a thermal strain εₜ = αΔT. Step 2: Here ΔT = 100°C, so εₜ = 10⁻⁵ × 100 = 10⁻³. Step 3: Because thermal expansion is completely prevented, the induced compressive stress has magnitude σ = YαΔT. Step 4: σ = (0.5 × 10¹¹)(10⁻³) = 5 × 10⁷ N m⁻². Step 5: F = σA = (5 × 10⁷)(10⁻³) = 5 × 10⁴ N = 50 × 10³ N. Final answer: (A) 50 × 10³ N.