A steel rod of length 1 m and cross-sectional area 10⁻⁴ m² is heated from 0°C to 200°C without being allowed to extend or bend. The compressive force produced is ______ × 10⁴ N. [Young's modulus = 2 × 10¹¹ N m⁻², coefficient of linear expansion = 10⁻⁵ K⁻¹]
Physics · Circular Motion
JEE Mains 8 April 2023 Shift 2 Evening Shift

Question

A steel rod of length 1 m and cross-sectional area 10⁻⁴ m² is heated from 0°C to 200°C without being allowed to extend or bend. The compressive force produced is ______ × 10⁴ N. [Young's modulus = 2 × 10¹¹ N m⁻², coefficient of linear expansion = 10⁻⁵ K⁻¹]

Physics · Circular Motion

JEE Mains 8 April 2023 Shift 2 Evening Shift

G1 Physics · Accepted Answer

The rod is not allowed to expand, so the free thermal strain αΔT is converted into mechanical compressive strain. Stress: σ = YαΔT Given: Y = 2×10¹¹ N m⁻² α = 10⁻⁵ K⁻¹ ΔT = 200 K Therefore, σ = (2×10¹¹)(10⁻⁵)(200) = 4×10⁸ N m⁻² Force: F = σA = (4×10⁸)(10⁻⁴) = 4×10⁴ N Final value: 4