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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)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A steel rod 10 mm in diameter and 1m long is heated from 20 °C to...
It will be compressive as elongation restricted.
Most Upvoted Answer
A steel rod 10 mm in diameter and 1m long is heated from 20 °C to...
Solution:
Given data:
Diameter of steel rod (d) = 10 mm
Length of rod (L) = 1 m
Change in temperature (ΔT) = 120 - 20 = 100 C
Modulus of elasticity (E) = 200 GPa = 2 × 10¹¹ N/m²
Coefficient of thermal expansion (α) = 12 × 10⁻⁶ per C
Formula used:
Thermal stress (σ) = E × α × ΔT
Explanation:
The thermal stress developed in a material subjected to a temperature change can be calculated using the above formula.
Here, the diameter of the steel rod is given instead of the cross-sectional area. Hence, we need to find the cross-sectional area of the rod first.
Cross-sectional area (A) = π/4 × d²
= π/4 × (10 mm)²
= 78.54 mm²
Now, we can substitute the given values in the formula to find the thermal stress.
σ = E × α × ΔT
= 2 × 10¹¹ N/m² × 12 × 10⁻⁶ per C × 100 C
= 240 MPa (compressive)
Therefore, the correct answer is option D, i.e., 240 MPa (compressive).
Conclusion:
When a steel rod is heated, it expands due to thermal expansion. If the rod is not free to expand, thermal stress is developed in the material. The magnitude and nature of the stress depend on the properties of the material and the amount of temperature change. In this case, the steel rod is subjected to a temperature change of 100 C, and the resulting thermal stress is 240 MPa (compressive).
Given data:
Diameter of steel rod (d) = 10 mm
Length of rod (L) = 1 m
Change in temperature (ΔT) = 120 - 20 = 100 C
Modulus of elasticity (E) = 200 GPa = 2 × 10¹¹ N/m²
Coefficient of thermal expansion (α) = 12 × 10⁻⁶ per C
Formula used:
Thermal stress (σ) = E × α × ΔT
Explanation:
The thermal stress developed in a material subjected to a temperature change can be calculated using the above formula.
Here, the diameter of the steel rod is given instead of the cross-sectional area. Hence, we need to find the cross-sectional area of the rod first.
Cross-sectional area (A) = π/4 × d²
= π/4 × (10 mm)²
= 78.54 mm²
Now, we can substitute the given values in the formula to find the thermal stress.
σ = E × α × ΔT
= 2 × 10¹¹ N/m² × 12 × 10⁻⁶ per C × 100 C
= 240 MPa (compressive)
Therefore, the correct answer is option D, i.e., 240 MPa (compressive).
Conclusion:
When a steel rod is heated, it expands due to thermal expansion. If the rod is not free to expand, thermal stress is developed in the material. The magnitude and nature of the stress depend on the properties of the material and the amount of temperature change. In this case, the steel rod is subjected to a temperature change of 100 C, and the resulting thermal stress is 240 MPa (compressive).
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Community Answer
A steel rod 10 mm in diameter and 1m long is heated from 20 °C to...
thermal stress = E α ∆T = 200 x 10^3 x 12 x 10 ^-6 x (120 - 20) = 240 Mpa since the rod is restricted the stress will be compressive
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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)Correct answer is option 'D'. Can you explain this answer? 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 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)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)Correct answer is option 'D'. Can you explain this answer?.
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)Correct answer is option 'D'. Can you explain this answer? 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 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)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)Correct answer is option 'D'. Can you explain this answer?.
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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)Correct answer is option 'D'. Can you explain this answer?, a detailed solution for 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)Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of 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)Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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