Question

A rod of material with Young's Modulus 200 GPa and coefficient of thermal expansion  \(= 0.001 \), \(^\circ \mathrm{C}^{-1}\)  is fixed at both ends and uniformly heated such that the rise in temperature is \(50 , ^\circ \mathrm{C}\). The stress developed in the rod is:  

• A. 1000 N/mm\(^2\)
• B. \(\geq\) 100000 N/mm\(^2\)
• C. 5000 N/mm\(^2\)
• D. 500 N/mm\(^2\)

Hint:

Thermal stress arises in constrained bodies — no expansion allowed.

Answer 1

The Correct Option is A

Thermal stress = \( E \cdot \alpha \cdot \Delta T = 200 \times 10^3 \cdot 0.001 \cdot 50 = 10000 \, \text{N/cm}^2 = 1000 \, \text{N/mm}^2 \)