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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 ______.
Options
100 × 103 N
2 × 103 N
5 × 103 N
50 × 103 N
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Solution
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.
