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 of bending. The compressive force developed in it is ______.

विकल्प

• 100 × 10³ N

• 2 × 10³ N

• 5 × 10³ N

• 50 × 10³ N

Answer 1

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 of bending. The compressive force developed in it is 50 × 10³ N.

Explanation:

Given: Young’s modulus (Y) = 0.5 × 10¹¹ N m⁻²

Coefficient of linear thermal expansion (α) = 10⁻⁵°C⁻¹

Cross-section area (A) = 10⁻³ m²

Change in temperature (ΔT) = 0°C to 100°C = 100° − 0° = 100°

Thermal stress (σ) = Y × ε

= YαΔT

= 0.5 × 10¹¹ × 10⁻⁵ × 100

= 0.5 × 10⁸ N m⁻²

The compressive force (F) = σ × A

= 0.5 × 10⁸ × 10⁻⁵

= 0.5 × 10⁵ N

= 50 × 10³ N

∴ The compressive force developed in the metallic bar is 50 × 10³ N.