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A metal rod is rigidly fixed at its both ends. The temperature of the rod has increased by 100℃. If the coefficient of linear expansion and elastic modulus of the metal rod are 10 x 10−6/℃ and 200GPa respectively, then what is the stress produced in the rod?
- a)100 MPa (tensile)
- b)200 MPa (tensile)
- c)200 MPa (compressive)
- d)100 MPa (compressive)
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A metal rod is rigidly fixed at its both ends. The temperature of the...
Α = 10 x 10-6/0C
∆t = 100℃
E = 200 GPa = 200 x 103 MPa
If the temperature of the rod is increased, the rod will try to elongate. But due to rigid fixed support, it will not elongate and compressive stress acts on it.
σ = Eα∆t = 200 x 103 x 10 x 10−6 x 100
= 200 MPa (compressive)
This question is part of UPSC exam. View all Mechanical Engineering courses
Most Upvoted Answer
A metal rod is rigidly fixed at its both ends. The temperature of the...
Given data:
Coefficient of linear expansion, α = 10 x 10^-6/℃
Elastic modulus, E = 200 GPa
Change in temperature, ΔT = 100℃
To find: Stress produced in the rod.
Formula:
The stress produced in a material due to thermal expansion is given by the formula:
σ = E α ΔT
Where,
σ = Stress produced
E = Elastic modulus of the material
α = Coefficient of linear expansion of the material
ΔT = Change in temperature
Calculation:
Substituting the given values in the formula, we get:
σ = E α ΔT
σ = 200 x 10^9 Pa x 10 x 10^-6/℃ x 100℃
σ = 200 MPa (compressive)
Therefore, the stress produced in the rod is 200 MPa (compressive).
Conclusion:
When a metal rod is heated, it expands due to thermal expansion. This expansion creates stress in the rod, which can be calculated using the above formula. In this case, the stress produced in the rod is compressive, as the metal contracts upon cooling.
Coefficient of linear expansion, α = 10 x 10^-6/℃
Elastic modulus, E = 200 GPa
Change in temperature, ΔT = 100℃
To find: Stress produced in the rod.
Formula:
The stress produced in a material due to thermal expansion is given by the formula:
σ = E α ΔT
Where,
σ = Stress produced
E = Elastic modulus of the material
α = Coefficient of linear expansion of the material
ΔT = Change in temperature
Calculation:
Substituting the given values in the formula, we get:
σ = E α ΔT
σ = 200 x 10^9 Pa x 10 x 10^-6/℃ x 100℃
σ = 200 MPa (compressive)
Therefore, the stress produced in the rod is 200 MPa (compressive).
Conclusion:
When a metal rod is heated, it expands due to thermal expansion. This expansion creates stress in the rod, which can be calculated using the above formula. In this case, the stress produced in the rod is compressive, as the metal contracts upon cooling.
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A metal rod is rigidly fixed at its both ends. The temperature of the rod has increased by 100℃. If the coefficient of linear expansion and elastic modulus of the metal rod are 10 x 10−6/℃ and 200GPa respectively, then what is the stress produced in the rod?a) 100 MPa (tensile)b) 200 MPa (tensile)c) 200 MPa (compressive)d) 100 MPa (compressive)Correct answer is option 'C'. Can you explain this answer?
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A metal rod is rigidly fixed at its both ends. The temperature of the rod has increased by 100℃. If the coefficient of linear expansion and elastic modulus of the metal rod are 10 x 10−6/℃ and 200GPa respectively, then what is the stress produced in the rod?a) 100 MPa (tensile)b) 200 MPa (tensile)c) 200 MPa (compressive)d) 100 MPa (compressive)Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A metal rod is rigidly fixed at its both ends. The temperature of the rod has increased by 100℃. If the coefficient of linear expansion and elastic modulus of the metal rod are 10 x 10−6/℃ and 200GPa respectively, then what is the stress produced in the rod?a) 100 MPa (tensile)b) 200 MPa (tensile)c) 200 MPa (compressive)d) 100 MPa (compressive)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A metal rod is rigidly fixed at its both ends. The temperature of the rod has increased by 100℃. If the coefficient of linear expansion and elastic modulus of the metal rod are 10 x 10−6/℃ and 200GPa respectively, then what is the stress produced in the rod?a) 100 MPa (tensile)b) 200 MPa (tensile)c) 200 MPa (compressive)d) 100 MPa (compressive)Correct answer is option 'C'. Can you explain this answer?.
A metal rod is rigidly fixed at its both ends. The temperature of the rod has increased by 100℃. If the coefficient of linear expansion and elastic modulus of the metal rod are 10 x 10−6/℃ and 200GPa respectively, then what is the stress produced in the rod?a) 100 MPa (tensile)b) 200 MPa (tensile)c) 200 MPa (compressive)d) 100 MPa (compressive)Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A metal rod is rigidly fixed at its both ends. The temperature of the rod has increased by 100℃. If the coefficient of linear expansion and elastic modulus of the metal rod are 10 x 10−6/℃ and 200GPa respectively, then what is the stress produced in the rod?a) 100 MPa (tensile)b) 200 MPa (tensile)c) 200 MPa (compressive)d) 100 MPa (compressive)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A metal rod is rigidly fixed at its both ends. The temperature of the rod has increased by 100℃. If the coefficient of linear expansion and elastic modulus of the metal rod are 10 x 10−6/℃ and 200GPa respectively, then what is the stress produced in the rod?a) 100 MPa (tensile)b) 200 MPa (tensile)c) 200 MPa (compressive)d) 100 MPa (compressive)Correct answer is option 'C'. Can you explain this answer?.
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