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If the elastic limit of copper is 1.5 × 108 N/ m2, determine the minimum diameter a copper wire can have under a load of 10.0 kg if its elastic limit is not to be exceeded.
- a)1.012 mm
- b)0.912 mm
- c)0.712 mm
- d)0.812 mm
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If the elastic limit of copper is 1.5× 108 N/ m2, determine the minimu...
Understanding the Problem
To determine the minimum diameter of a copper wire under a load of 10.0 kg without exceeding its elastic limit, we will use the relationship between stress, force, and area.
Key Concepts
- Elastic Limit of Copper: 1.5 × 10^8 N/m²
- Load (Weight): 10 kg
- Force Calculation: Weight (Force) = mass × gravity
Step-by-Step Calculation
1. Calculate the Force (Weight):
- Weight = mass × gravity = 10 kg × 9.81 m/s² = 98.1 N
2. Determine the Required Area (A):
- Stress (σ) = Force (F) / Area (A)
- Rearranging gives: A = F / σ
- A = 98.1 N / (1.5 × 10^8 N/m²) = 6.54 × 10^-7 m²
3. Relating Area to Diameter:
- Area of a circle: A = π(d² / 4)
- Rearranging gives: d² = (4A) / π
- Thus, d = sqrt((4 × 6.54 × 10^-7) / π)
4. Calculate Diameter:
- d ≈ 0.912 mm
Conclusion
The minimum diameter of the copper wire that can safely support a load of 10 kg without exceeding its elastic limit is approximately 0.912 mm. Thus, the correct answer is option 'B'.
This calculation highlights the importance of material properties and dimensions in engineering applications to ensure safety and functionality.
To determine the minimum diameter of a copper wire under a load of 10.0 kg without exceeding its elastic limit, we will use the relationship between stress, force, and area.
Key Concepts
- Elastic Limit of Copper: 1.5 × 10^8 N/m²
- Load (Weight): 10 kg
- Force Calculation: Weight (Force) = mass × gravity
Step-by-Step Calculation
1. Calculate the Force (Weight):
- Weight = mass × gravity = 10 kg × 9.81 m/s² = 98.1 N
2. Determine the Required Area (A):
- Stress (σ) = Force (F) / Area (A)
- Rearranging gives: A = F / σ
- A = 98.1 N / (1.5 × 10^8 N/m²) = 6.54 × 10^-7 m²
3. Relating Area to Diameter:
- Area of a circle: A = π(d² / 4)
- Rearranging gives: d² = (4A) / π
- Thus, d = sqrt((4 × 6.54 × 10^-7) / π)
4. Calculate Diameter:
- d ≈ 0.912 mm
Conclusion
The minimum diameter of the copper wire that can safely support a load of 10 kg without exceeding its elastic limit is approximately 0.912 mm. Thus, the correct answer is option 'B'.
This calculation highlights the importance of material properties and dimensions in engineering applications to ensure safety and functionality.
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Community Answer
If the elastic limit of copper is 1.5× 108 N/ m2, determine the minimu...
Elastic limit (allowable stress) of copper, σel =1.5 ×108 N m−2
Load m =10.0 kg ⇒ F = mg =10.0 × 9.8 = 98 N
Load m =10.0 kg ⇒ F = mg =10.0 × 9.8 = 98 N
So, Option B is the correct answer.
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Question Description
If the elastic limit of copper is 1.5× 108 N/ m2, determine the minimum diameter a copper wire can have under a load of 10.0 kg if its elastic limit is not to be exceeded.a)1.012 mmb)0.912 mmc)0.712 mmd)0.812 mmCorrect answer is option 'B'. Can you explain this answer? for NEET 2026 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If the elastic limit of copper is 1.5× 108 N/ m2, determine the minimum diameter a copper wire can have under a load of 10.0 kg if its elastic limit is not to be exceeded.a)1.012 mmb)0.912 mmc)0.712 mmd)0.812 mmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the elastic limit of copper is 1.5× 108 N/ m2, determine the minimum diameter a copper wire can have under a load of 10.0 kg if its elastic limit is not to be exceeded.a)1.012 mmb)0.912 mmc)0.712 mmd)0.812 mmCorrect answer is option 'B'. Can you explain this answer?.
If the elastic limit of copper is 1.5× 108 N/ m2, determine the minimum diameter a copper wire can have under a load of 10.0 kg if its elastic limit is not to be exceeded.a)1.012 mmb)0.912 mmc)0.712 mmd)0.812 mmCorrect answer is option 'B'. Can you explain this answer? for NEET 2026 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If the elastic limit of copper is 1.5× 108 N/ m2, determine the minimum diameter a copper wire can have under a load of 10.0 kg if its elastic limit is not to be exceeded.a)1.012 mmb)0.912 mmc)0.712 mmd)0.812 mmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the elastic limit of copper is 1.5× 108 N/ m2, determine the minimum diameter a copper wire can have under a load of 10.0 kg if its elastic limit is not to be exceeded.a)1.012 mmb)0.912 mmc)0.712 mmd)0.812 mmCorrect answer is option 'B'. Can you explain this answer?.
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