A metallic bar of Young's modulus, 0.5 × 10¹¹ N m⁻² and coefficient of linear thermal expansion 10⁻⁵ ⁻¹, length 1 m and area of cross-section 10⁻³ m² is heated from 0 to 100 without expansion or bending. The compressive force developed in it is: (a) 5 × 10³ N (b) 50 × 10³ N (c) 100 × 10³ N (d) 2 × 10³ N

Answer: (b). Thermal force when expansion is prevented: F = YAαΔ T. F = 0.5 × 10¹¹ × 10⁻³ × 10⁻⁵ × 100 = 5 × 10⁴ N So the answer is (b) 50 × 10³ N.

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Thermal Stress & Breaking Stress

A metallic bar of Young's modulus, $0.5 \times 10^{11}\text{ N m}^{-2}$ and coefficient of linear thermal expansion $10^{-5}\,{}^\circ\text{C}^{-1}$ , length $1\text{ m}$ and area of cross-section $10^{-3}\text{ m}^2$ is heated from $0^\circ\text{C}$ to $100^\circ\text{C}$ without expansion or bending. The compressive force developed in it is:

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Answer: (b)

Thermal force when expansion is prevented: $F = YA\alpha\Delta T$ .
$F = 0.5 \times 10^{11} \times 10^{-3} \times 10^{-5} \times 100 = 5 \times 10^4\text{ N}$
So the answer is (b) $50 \times 10^3\text{ N}$ .

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