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

The Correct Option is B

Step 1: Use the Formula for Thermal Stress 

Thermal stress is given by:

$$ F = Y \alpha \Delta T A $$

\( Y \) = Young’s modulus

\( \alpha \) = Coefficient of linear thermal expansion

\( \Delta T \) = Temperature change

\( A \) = Area of cross-section

Step 2: Substitute the Given Values

Given:

\( Y = 0.5 \times 10^{11} \) N/m²

\( \alpha = 10^{-5} \) °C\(^{-1}\)

\( \Delta T = 100 \)°C

\( A = 10^{-3} \) m²

Substituting these values into the formula:

$$ F = (0.5 \times 10^{11}) (10^{-5}) (100) (10^{-3}) $$

Step 3: Simplify

$$ F = 0.5 \times 10^3 \times 100 $$

$$ F = 50 \times 10^3 \text{ N} $$

Step 4: Conclusion

The compressive force developed is 50 × 10³ N.