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Assume that young's modulus of a wire of length L and radius 'r' is Y. If length is reduced to L/2 and radius r/2 then what will be its young's modulus?
- a)halved
- b)doubled
- c)unaffected
- d)One-fourth of its original value
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Assume that young's modulus of a wire of length L and radius '...
Young's is a property of the material of construction of a wire. It depends only on the nature of the material used for making the wire.
Young's modulus does not depend on the physical dimensions such as the length and diameter of wire. Thus there will be no change in Young's modulus.
Most Upvoted Answer
Assume that young's modulus of a wire of length L and radius '...
Young's modulus (Y) is a measure of the stiffness of a material and is defined as the ratio of stress to strain. When the length and radius of a wire are changed, the Young's modulus of the wire remains unaffected.
Explanation:
- The Young's modulus (Y) is given by the formula:
Y = stress / strain
- The stress (σ) is defined as the force (F) applied to the wire divided by its cross-sectional area (A):
σ = F / A
- The strain (ε) is defined as the change in length (ΔL) divided by the original length (L):
ε = ΔL / L
- When the length of the wire is reduced to L/2 and the radius is reduced to r/2, the force applied to the wire and the cross-sectional area remain the same. Therefore, the stress remains unchanged.
- The change in length (ΔL) can be calculated using the formula:
ΔL = ε * L
- Substituting the values, we get:
ΔL = (L/2 - L) = -L/2
- Since the length is reduced, the change in length is negative.
- The strain (ε) is given by:
ε = ΔL / L = -L/2 / L = -1/2
- Now, substituting the values of stress and strain in the formula for Young's modulus, we get:
Y = σ / ε = (F / A) / (-1/2) = -2F/A
- We can see that the Young's modulus is a ratio of the stress to the strain, and the negative sign indicates that the wire is under compressive stress.
- As the length and radius of the wire are changed, the Young's modulus remains unaffected. Therefore, the correct answer is option 'C': unaffected.
Explanation:
- The Young's modulus (Y) is given by the formula:
Y = stress / strain
- The stress (σ) is defined as the force (F) applied to the wire divided by its cross-sectional area (A):
σ = F / A
- The strain (ε) is defined as the change in length (ΔL) divided by the original length (L):
ε = ΔL / L
- When the length of the wire is reduced to L/2 and the radius is reduced to r/2, the force applied to the wire and the cross-sectional area remain the same. Therefore, the stress remains unchanged.
- The change in length (ΔL) can be calculated using the formula:
ΔL = ε * L
- Substituting the values, we get:
ΔL = (L/2 - L) = -L/2
- Since the length is reduced, the change in length is negative.
- The strain (ε) is given by:
ε = ΔL / L = -L/2 / L = -1/2
- Now, substituting the values of stress and strain in the formula for Young's modulus, we get:
Y = σ / ε = (F / A) / (-1/2) = -2F/A
- We can see that the Young's modulus is a ratio of the stress to the strain, and the negative sign indicates that the wire is under compressive stress.
- As the length and radius of the wire are changed, the Young's modulus remains unaffected. Therefore, the correct answer is option 'C': unaffected.
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Assume that young's modulus of a wire of length L and radius 'r' is Y. If length is reduced to L/2 and radius r/2 then what will be its young's modulus?a)halvedb)doubledc)unaffectedd)One-fourth of its original valueCorrect answer is option 'C'. 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 Assume that young's modulus of a wire of length L and radius 'r' is Y. If length is reduced to L/2 and radius r/2 then what will be its young's modulus?a)halvedb)doubledc)unaffectedd)One-fourth of its original valueCorrect answer is option 'C'. 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 Assume that young's modulus of a wire of length L and radius 'r' is Y. If length is reduced to L/2 and radius r/2 then what will be its young's modulus?a)halvedb)doubledc)unaffectedd)One-fourth of its original valueCorrect answer is option 'C'. Can you explain this answer?.
Assume that young's modulus of a wire of length L and radius 'r' is Y. If length is reduced to L/2 and radius r/2 then what will be its young's modulus?a)halvedb)doubledc)unaffectedd)One-fourth of its original valueCorrect answer is option 'C'. 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 Assume that young's modulus of a wire of length L and radius 'r' is Y. If length is reduced to L/2 and radius r/2 then what will be its young's modulus?a)halvedb)doubledc)unaffectedd)One-fourth of its original valueCorrect answer is option 'C'. 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 Assume that young's modulus of a wire of length L and radius 'r' is Y. If length is reduced to L/2 and radius r/2 then what will be its young's modulus?a)halvedb)doubledc)unaffectedd)One-fourth of its original valueCorrect answer is option 'C'. Can you explain this answer?.
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