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Can you explain the answer of this question below:
A steel rod 10 mm in diameter and 1m long is heated from 20 °C to 120°C, E = 200 GPa and α = 12 × 10-6 per °C. If the rod is not free to expand, the thermal stress developed is:
- A:120 MPa (tensile)
- B:240 MPa (tensile)
- C:120 MPa (compressive)
- D:240 MPa (compressive)
The answer is d.
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Can you explain the answer of this question below:A steel rod 10 mm in...
It will be compressive as elongation restricted.
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Can you explain the answer of this question below:A steel rod 10 mm in...
Given Data:
- Diameter of steel rod: 10 mm
- Length of steel rod: 1 m
- Initial temperature: 20 °C
- Final temperature: 120 °C
- Young's modulus (E) of steel: 200 GPa
- Coefficient of linear expansion (α) of steel: 12 × 10^-6 per °C
Calculating Thermal Expansion:
The thermal expansion of a material can be calculated using the formula:
ΔL = L * α * ΔT
Where:
ΔL is the change in length
L is the original length
α is the coefficient of linear expansion
ΔT is the change in temperature
In this case, the change in length can be calculated as:
ΔL = 1 m * 12 × 10^-6 per °C * (120 °C - 20 °C)
= 1 m * 12 × 10^-6 per °C * 100 °C
= 0.0012 m
Calculating Cross-sectional Area:
The cross-sectional area of a rod can be calculated using the formula:
A = π * (d/2)^2
Where:
A is the cross-sectional area
d is the diameter of the rod
In this case, the cross-sectional area can be calculated as:
A = π * (10 mm/2)^2
= π * 5 mm^2
= 15.71 mm^2
Calculating Thermal Stress:
The thermal stress developed in a rod can be calculated using the formula:
σ = E * α * ΔT
Where:
σ is the thermal stress
E is the Young's modulus
α is the coefficient of linear expansion
ΔT is the change in temperature
In this case, the thermal stress can be calculated as:
σ = 200 GPa * 12 × 10^-6 per °C * (120 °C - 20 °C)
= 200 GPa * 12 × 10^-6 per °C * 100 °C
= 240 MPa
Conclusion:
The thermal stress developed in the steel rod when heated from 20 °C to 120 °C and not allowed to expand is 240 MPa (compressive). Therefore, the correct answer is option D: 240 MPa (compressive).
- Diameter of steel rod: 10 mm
- Length of steel rod: 1 m
- Initial temperature: 20 °C
- Final temperature: 120 °C
- Young's modulus (E) of steel: 200 GPa
- Coefficient of linear expansion (α) of steel: 12 × 10^-6 per °C
Calculating Thermal Expansion:
The thermal expansion of a material can be calculated using the formula:
ΔL = L * α * ΔT
Where:
ΔL is the change in length
L is the original length
α is the coefficient of linear expansion
ΔT is the change in temperature
In this case, the change in length can be calculated as:
ΔL = 1 m * 12 × 10^-6 per °C * (120 °C - 20 °C)
= 1 m * 12 × 10^-6 per °C * 100 °C
= 0.0012 m
Calculating Cross-sectional Area:
The cross-sectional area of a rod can be calculated using the formula:
A = π * (d/2)^2
Where:
A is the cross-sectional area
d is the diameter of the rod
In this case, the cross-sectional area can be calculated as:
A = π * (10 mm/2)^2
= π * 5 mm^2
= 15.71 mm^2
Calculating Thermal Stress:
The thermal stress developed in a rod can be calculated using the formula:
σ = E * α * ΔT
Where:
σ is the thermal stress
E is the Young's modulus
α is the coefficient of linear expansion
ΔT is the change in temperature
In this case, the thermal stress can be calculated as:
σ = 200 GPa * 12 × 10^-6 per °C * (120 °C - 20 °C)
= 200 GPa * 12 × 10^-6 per °C * 100 °C
= 240 MPa
Conclusion:
The thermal stress developed in the steel rod when heated from 20 °C to 120 °C and not allowed to expand is 240 MPa (compressive). Therefore, the correct answer is option D: 240 MPa (compressive).
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Can you explain the answer of this question below:A steel rod 10 mm in...
It will be compressive as elongation restricted.
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Can you explain the answer of this question below:A steel rod 10 mm in diameter and 1m long is heated from 20 °C to 120°C, E = 200 GPa and α = 12 × 10-6 per °C. If the rod is not free to expand, the thermal stress developed is:A:120 MPa (tensile)B:240 MPa (tensile)C:120 MPa (compressive)D:240 MPa (compressive)The answer is d. for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Can you explain the answer of this question below:A steel rod 10 mm in diameter and 1m long is heated from 20 °C to 120°C, E = 200 GPa and α = 12 × 10-6 per °C. If the rod is not free to expand, the thermal stress developed is:A:120 MPa (tensile)B:240 MPa (tensile)C:120 MPa (compressive)D:240 MPa (compressive)The answer is d. covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Can you explain the answer of this question below:A steel rod 10 mm in diameter and 1m long is heated from 20 °C to 120°C, E = 200 GPa and α = 12 × 10-6 per °C. If the rod is not free to expand, the thermal stress developed is:A:120 MPa (tensile)B:240 MPa (tensile)C:120 MPa (compressive)D:240 MPa (compressive)The answer is d..
Can you explain the answer of this question below:A steel rod 10 mm in diameter and 1m long is heated from 20 °C to 120°C, E = 200 GPa and α = 12 × 10-6 per °C. If the rod is not free to expand, the thermal stress developed is:A:120 MPa (tensile)B:240 MPa (tensile)C:120 MPa (compressive)D:240 MPa (compressive)The answer is d. for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Can you explain the answer of this question below:A steel rod 10 mm in diameter and 1m long is heated from 20 °C to 120°C, E = 200 GPa and α = 12 × 10-6 per °C. If the rod is not free to expand, the thermal stress developed is:A:120 MPa (tensile)B:240 MPa (tensile)C:120 MPa (compressive)D:240 MPa (compressive)The answer is d. covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Can you explain the answer of this question below:A steel rod 10 mm in diameter and 1m long is heated from 20 °C to 120°C, E = 200 GPa and α = 12 × 10-6 per °C. If the rod is not free to expand, the thermal stress developed is:A:120 MPa (tensile)B:240 MPa (tensile)C:120 MPa (compressive)D:240 MPa (compressive)The answer is d..
Solutions for Can you explain the answer of this question below:A steel rod 10 mm in diameter and 1m long is heated from 20 °C to 120°C, E = 200 GPa and α = 12 × 10-6 per °C. If the rod is not free to expand, the thermal stress developed is:A:120 MPa (tensile)B:240 MPa (tensile)C:120 MPa (compressive)D:240 MPa (compressive)The answer is d. in English & in Hindi are available as part of our courses for Mechanical Engineering.
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