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 tension produced in the rod is______ ×10⁴N. (Given Young's modulus of steel = 2×10¹¹ Nm^-2, coefficient of linear expansion = 10^-5K^-1)

Answer 1

Correct Answer: 4

The thermal stress in the rod is given by: \[ \text{Stress} = Y \alpha \Delta T, \] where: 
 \( Y = 2 \times 10^{11} \, \text{N/m}^2 \) (Young's modulus), 
 \( \alpha = 10^{-5} \, \text{K}^{-1} \) (coefficient of linear expansion), 
 \( \Delta T = 200 \, \text{K} \) (temperature change). 
The force due to thermal stress is: \[ F = \text{Stress} \cdot A = Y \alpha \Delta T \cdot A. \] Substitute \( A = 10^{-4} \, \text{m}^2 \): \[ F = (2 \times 10^{11}) (10^{-5}) (200) (10^{-4}). \] Simplify: \[ F = 4 \times 10^4 \, \text{N}. \] 
Final Answer: The compressive tension produced in the rod is: \[ \boxed{4 \times 10^4 \, \text{N}}. \]