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 :

• A. 5 × 103 N
• B. 50 × 103 N
• C. 100 × 103 N
• D. 2 × 103 N

Answer 1

Answer: (B)

50 × 103 N

Answer 2

Thermal stress is:
$\text{Stress} = Y \cdot \alpha \cdot \Delta T$.
The force is:
$F = \text{Stress} \cdot A = Y \cdot \alpha \cdot \Delta T \cdot A$.
Substituting values:
$F = 0.5 \times 10^{11} \cdot 10^{-5} \cdot 100 \cdot 10^{-3} = 50 \times 10^3 \, N$.