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An elastic bar of length L, uniform cross sectional area A, coefficient of thermal expansion α, and Young’s modulus E is fixed at the two ends. The temperature of the bar is increased by T, resulting in an axial stress σ. Keeping all other parameters unchanged, if the length of the bar is doubled, the axial stress would be  
  • a)
    σ  
  • b)
    2 σ
  • c)
    0.5 σ
  • d)
    0.25 α σ
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
An elastic bar of length L, uniform cross sectional area A, coefficien...
σ varies with ∆T and does not depends upon the length of bar. 
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Most Upvoted Answer
An elastic bar of length L, uniform cross sectional area A, coefficien...
Explanation:

Given:
- Length of the bar = L
- Cross-sectional area of the bar = A
- Coefficient of thermal expansion = α
- Young's modulus = E
- Increase in temperature = T
- Axial stress = σ

Formula:
The axial stress can be calculated using the formula:

σ = α * E * ΔT

where ΔT is the change in temperature.

Analysis:
1. Let's consider the original bar with length L and temperature increase ΔT. The axial stress in the bar is given by σ = α * E * ΔT.
2. Now, if the length of the bar is doubled, the new length becomes 2L.
3. The temperature increase remains the same, ΔT.
4. The cross-sectional area of the bar, A, and the coefficient of thermal expansion, α, remain unchanged.
5. Using the formula for the axial stress, the new axial stress σ' can be calculated as σ' = α * E * ΔT.
6. Comparing the two equations, σ and σ', we can see that the only difference is the length of the bar. All other parameters are the same.
7. Therefore, the axial stress, σ', in the bar with double the length will be twice the axial stress, σ, in the original bar.

Conclusion:
- The axial stress in the bar with double the length will be twice the axial stress in the original bar. Therefore, the correct answer is option 'A' - 2.
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An elastic bar of length L, uniform cross sectional area A, coefficient of thermal expansion α, and Young’s modulus E is fixed at the two ends. The temperature of the bar is increased by T, resulting in an axial stress σ. Keeping all other parameters unchanged, if the length of the bar is doubled, the axial stress would be a)σ b)2 σc)0.5 σd)0.25 α σCorrect answer is option 'A'. Can you explain this answer?
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