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Calculate the Percentage increase in length of a wire of a diameter 1 mm streched by a force of half kilograms weight.young modules of wire is 12*10¹¹dyne/cm²?
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Calculate the Percentage increase in length of a wire of a diameter 1 ...
Calculating Percentage Increase in Length of a Wire
To determine the percentage increase in the length of a wire stretched by a force, we can use the formula derived from Young's modulus. Let's break down the calculation.
Given Data:
- Diameter of the wire (d) = 1 mm = 0.1 cm
- Radius of the wire (r) = d/2 = 0.05 cm
- Force (F) = 0.5 kg weight = 0.5 * 980 dyne (since 1 kg = 980 dyne) = 490 dyne
- Young's modulus (Y) = 12 * 10^11 dyne/cm²
- Original length of the wire (L) = L (assumed as 1 cm for calculation)
Steps to Calculate:
1. Calculate the Cross-sectional Area (A):
- A = πr²
- A = π(0.05)² = π(0.0025) cm² ≈ 0.00785 cm²
2. Calculate the Stress (σ):
- σ = F/A
- σ = 490 dyne / 0.00785 cm² ≈ 62468.3 dyne/cm²
3. Calculate the Strain (ε):
- Using Young's modulus formula: Y = σ/ε
- ε = σ/Y = 62468.3 dyne/cm² / (12 * 10^11 dyne/cm²) ≈ 5.2069 * 10^(-7)
4. Calculate the Change in Length (ΔL):
- ΔL = ε * L
- ΔL = 5.2069 * 10^(-7) * 1 cm ≈ 5.2069 * 10^(-7) cm
5. Calculate the Percentage Increase:
- Percentage increase = (ΔL/L) * 100
- Percentage increase = (5.2069 * 10^(-7) / 1) * 100 ≈ 5.2069 * 10^(-5)%
Conclusion:
The percentage increase in length of the wire when stretched by a force of half a kilogram is approximately 0.00005207%. This negligible increase illustrates the high rigidity of the material, as indicated by the Young's modulus value.
To determine the percentage increase in the length of a wire stretched by a force, we can use the formula derived from Young's modulus. Let's break down the calculation.
Given Data:
- Diameter of the wire (d) = 1 mm = 0.1 cm
- Radius of the wire (r) = d/2 = 0.05 cm
- Force (F) = 0.5 kg weight = 0.5 * 980 dyne (since 1 kg = 980 dyne) = 490 dyne
- Young's modulus (Y) = 12 * 10^11 dyne/cm²
- Original length of the wire (L) = L (assumed as 1 cm for calculation)
Steps to Calculate:
1. Calculate the Cross-sectional Area (A):
- A = πr²
- A = π(0.05)² = π(0.0025) cm² ≈ 0.00785 cm²
2. Calculate the Stress (σ):
- σ = F/A
- σ = 490 dyne / 0.00785 cm² ≈ 62468.3 dyne/cm²
3. Calculate the Strain (ε):
- Using Young's modulus formula: Y = σ/ε
- ε = σ/Y = 62468.3 dyne/cm² / (12 * 10^11 dyne/cm²) ≈ 5.2069 * 10^(-7)
4. Calculate the Change in Length (ΔL):
- ΔL = ε * L
- ΔL = 5.2069 * 10^(-7) * 1 cm ≈ 5.2069 * 10^(-7) cm
5. Calculate the Percentage Increase:
- Percentage increase = (ΔL/L) * 100
- Percentage increase = (5.2069 * 10^(-7) / 1) * 100 ≈ 5.2069 * 10^(-5)%
Conclusion:
The percentage increase in length of the wire when stretched by a force of half a kilogram is approximately 0.00005207%. This negligible increase illustrates the high rigidity of the material, as indicated by the Young's modulus value.
Community Answer
Calculate the Percentage increase in length of a wire of a diameter 1 ...
0.0013 percent
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Calculate the Percentage increase in length of a wire of a diameter 1 mm streched by a force of half kilograms weight.young modules of wire is 12*10¹¹dyne/cm²?
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Calculate the Percentage increase in length of a wire of a diameter 1 mm streched by a force of half kilograms weight.young modules of wire is 12*10¹¹dyne/cm²? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Calculate the Percentage increase in length of a wire of a diameter 1 mm streched by a force of half kilograms weight.young modules of wire is 12*10¹¹dyne/cm²? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the Percentage increase in length of a wire of a diameter 1 mm streched by a force of half kilograms weight.young modules of wire is 12*10¹¹dyne/cm²?.
Calculate the Percentage increase in length of a wire of a diameter 1 mm streched by a force of half kilograms weight.young modules of wire is 12*10¹¹dyne/cm²? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Calculate the Percentage increase in length of a wire of a diameter 1 mm streched by a force of half kilograms weight.young modules of wire is 12*10¹¹dyne/cm²? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the Percentage increase in length of a wire of a diameter 1 mm streched by a force of half kilograms weight.young modules of wire is 12*10¹¹dyne/cm²?.
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