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What diameter should a 10-m-long steel wire have if we do not want it to stretch more than 0.5 cm under a tension of 940 N? Take Young's modulus of steel as 20 × 1010 Pa
- a)3.2 mm
- b)3.0 mm
- c)3.4 mm
- d)3.6 mm
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
What diameter should a 10-m-long steel wire have if we do not want it ...
Y=F x l/A x Δ l
Δ l=0.5cm=0.5x10-2m, l=10M, F=940N
Y=20x1010pa
20x1010=940x10/πr2x0.5x10-10
πr2=94x100/5x10-3x2x1011=94x102/10x108
r2=94/π x 10-7 =2.99 x 10-6
r2 ≅3x10-6
r=1.13x10-10 m
diameter=2r=3.6mm
Δ l=0.5cm=0.5x10-2m, l=10M, F=940N
Y=20x1010pa
20x1010=940x10/πr2x0.5x10-10
πr2=94x100/5x10-3x2x1011=94x102/10x108
r2=94/π x 10-7 =2.99 x 10-6
r2 ≅3x10-6
r=1.13x10-10 m
diameter=2r=3.6mm
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What diameter should a 10-m-long steel wire have if we do not want it ...
Given:
- Length of steel wire = 10 m
- Tension applied = 940 N
- Maximum elongation allowed = 0.5 cm = 0.005 m
- Young's modulus of steel = 20 x 10^10 Pa
To find: Diameter of the steel wire
Formula used:
- Tension (T) = (π/4) x (d^2) x σ
- Elongation (ε) = (TL) / (A x E)
where,
- T = Tension applied
- d = Diameter of the wire
- σ = Stress
- ε = Elongation
- L = Length of the wire
- A = Cross-sectional area of the wire
- E = Young's modulus of the material
Solution:
1. Finding the stress applied on the wire:
From the formula, Tension (T) = (π/4) x (d^2) x σ, we can rearrange to find the stress (σ) as:
σ = (4 x T) / (π x d^2)
Substituting the given values, we get:
σ = (4 x 940) / (π x d^2) = 298.77 / d^2
2. Finding the cross-sectional area of the wire:
We know that the cross-sectional area (A) of a wire is given by:
A = (π/4) x d^2
3. Finding the elongation of the wire:
From the formula, Elongation (ε) = (TL) / (A x E), we can rearrange to find the diameter (d) as:
d = sqrt((4 x T x L) / (π x ε x E))
Substituting the given values, we get:
d = sqrt((4 x 940 x 10) / (π x 0.005 x 20 x 10^10)) = 0.0034 m = 3.4 mm
Therefore, the diameter of the steel wire should be 3.4 mm to ensure that it does not stretch more than 0.5 cm under a tension of 940 N.
- Length of steel wire = 10 m
- Tension applied = 940 N
- Maximum elongation allowed = 0.5 cm = 0.005 m
- Young's modulus of steel = 20 x 10^10 Pa
To find: Diameter of the steel wire
Formula used:
- Tension (T) = (π/4) x (d^2) x σ
- Elongation (ε) = (TL) / (A x E)
where,
- T = Tension applied
- d = Diameter of the wire
- σ = Stress
- ε = Elongation
- L = Length of the wire
- A = Cross-sectional area of the wire
- E = Young's modulus of the material
Solution:
1. Finding the stress applied on the wire:
From the formula, Tension (T) = (π/4) x (d^2) x σ, we can rearrange to find the stress (σ) as:
σ = (4 x T) / (π x d^2)
Substituting the given values, we get:
σ = (4 x 940) / (π x d^2) = 298.77 / d^2
2. Finding the cross-sectional area of the wire:
We know that the cross-sectional area (A) of a wire is given by:
A = (π/4) x d^2
3. Finding the elongation of the wire:
From the formula, Elongation (ε) = (TL) / (A x E), we can rearrange to find the diameter (d) as:
d = sqrt((4 x T x L) / (π x ε x E))
Substituting the given values, we get:
d = sqrt((4 x 940 x 10) / (π x 0.005 x 20 x 10^10)) = 0.0034 m = 3.4 mm
Therefore, the diameter of the steel wire should be 3.4 mm to ensure that it does not stretch more than 0.5 cm under a tension of 940 N.
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What diameter should a 10-m-long steel wire have if we do not want it to stretch more than 0.5 cm under a tension of 940 N? Take Young's modulus of steel as 20 × 1010 Paa)3.2 mmb)3.0 mmc)3.4 mmd)3.6 mmCorrect answer is option 'C'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about What diameter should a 10-m-long steel wire have if we do not want it to stretch more than 0.5 cm under a tension of 940 N? Take Young's modulus of steel as 20 × 1010 Paa)3.2 mmb)3.0 mmc)3.4 mmd)3.6 mmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What diameter should a 10-m-long steel wire have if we do not want it to stretch more than 0.5 cm under a tension of 940 N? Take Young's modulus of steel as 20 × 1010 Paa)3.2 mmb)3.0 mmc)3.4 mmd)3.6 mmCorrect answer is option 'C'. Can you explain this answer?.
What diameter should a 10-m-long steel wire have if we do not want it to stretch more than 0.5 cm under a tension of 940 N? Take Young's modulus of steel as 20 × 1010 Paa)3.2 mmb)3.0 mmc)3.4 mmd)3.6 mmCorrect answer is option 'C'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about What diameter should a 10-m-long steel wire have if we do not want it to stretch more than 0.5 cm under a tension of 940 N? Take Young's modulus of steel as 20 × 1010 Paa)3.2 mmb)3.0 mmc)3.4 mmd)3.6 mmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What diameter should a 10-m-long steel wire have if we do not want it to stretch more than 0.5 cm under a tension of 940 N? Take Young's modulus of steel as 20 × 1010 Paa)3.2 mmb)3.0 mmc)3.4 mmd)3.6 mmCorrect answer is option 'C'. Can you explain this answer?.
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What diameter should a 10-m-long steel wire have if we do not want it to stretch more than 0.5 cm under a tension of 940 N? Take Young's modulus of steel as 20 × 1010 Paa)3.2 mmb)3.0 mmc)3.4 mmd)3.6 mmCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for What diameter should a 10-m-long steel wire have if we do not want it to stretch more than 0.5 cm under a tension of 940 N? Take Young's modulus of steel as 20 × 1010 Paa)3.2 mmb)3.0 mmc)3.4 mmd)3.6 mmCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of What diameter should a 10-m-long steel wire have if we do not want it to stretch more than 0.5 cm under a tension of 940 N? Take Young's modulus of steel as 20 × 1010 Paa)3.2 mmb)3.0 mmc)3.4 mmd)3.6 mmCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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