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A tension member of square cross-section of side 10 mm and Young’s modulus E is to be replaced by another member of square cross-section of same length but Young’s modulus E/2. The side of the new square cross-section, required to maintain the same elongation under the same load, is nearly
- a)14 mm
- b)17 mm
- c)8 mm
- d)5 mm
Correct answer is option 'A'. Can you explain this answer?
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A tension member of square cross-section of side 10 mm and Young’s mo...
S= 14.14 mm
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A tension member of square cross-section of side 10 mm and Young’s mo...
To find the side length of the new square cross-section, we need to consider the relationship between the elongation, load, and Young's modulus.
Given data:
Original tension member:
- Side length: 10 mm
- Young's modulus: E
New tension member:
- Side length: ?
- Young's modulus: E/2
We need to find the side length of the new square cross-section that will maintain the same elongation under the same load.
Let's assume the original tension member is subjected to a load P, resulting in an elongation δ.
Now, let's consider the stress-strain relationship for the original member:
σ = E * ε
Where:
σ is the stress (force per unit area)
E is the Young's modulus
ε is the strain (change in length per unit length)
Since the load is the same for both members, the stress in the original member is equal to the stress in the new member:
σ1 = σ2
E * ε1 = (E/2) * ε2
Now, let's consider the strain relationship:
ε = δ / L
Where:
δ is the elongation
L is the original length
Since the elongation is the same for both members, we can equate the strains:
ε1 = ε2
δ1 / L1 = δ2 / L2
Since the lengths are the same for both members, we can simplify the equation:
δ1 = δ2
Now we can substitute this relationship back into the stress equation:
E * (δ1 / L1) = (E/2) * (δ1 / L2)
Simplifying:
2 * L2 = L1
Since the original length and the new length are the same, we can equate the side lengths of the squares:
2 * s = 10
s = 10 / 2 = 5 mm
Therefore, the side length of the new square cross-section required to maintain the same elongation under the same load is 5 mm.
Given data:
Original tension member:
- Side length: 10 mm
- Young's modulus: E
New tension member:
- Side length: ?
- Young's modulus: E/2
We need to find the side length of the new square cross-section that will maintain the same elongation under the same load.
Let's assume the original tension member is subjected to a load P, resulting in an elongation δ.
Now, let's consider the stress-strain relationship for the original member:
σ = E * ε
Where:
σ is the stress (force per unit area)
E is the Young's modulus
ε is the strain (change in length per unit length)
Since the load is the same for both members, the stress in the original member is equal to the stress in the new member:
σ1 = σ2
E * ε1 = (E/2) * ε2
Now, let's consider the strain relationship:
ε = δ / L
Where:
δ is the elongation
L is the original length
Since the elongation is the same for both members, we can equate the strains:
ε1 = ε2
δ1 / L1 = δ2 / L2
Since the lengths are the same for both members, we can simplify the equation:
δ1 = δ2
Now we can substitute this relationship back into the stress equation:
E * (δ1 / L1) = (E/2) * (δ1 / L2)
Simplifying:
2 * L2 = L1
Since the original length and the new length are the same, we can equate the side lengths of the squares:
2 * s = 10
s = 10 / 2 = 5 mm
Therefore, the side length of the new square cross-section required to maintain the same elongation under the same load is 5 mm.
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A tension member of square cross-section of side 10 mm and Young’s modulus E is to be replaced by another member of square cross-section of same length but Young’s modulus E/2. The side of the new square cross-section, required to maintain the same elongation under the same load, is nearlya)14 mmb)17 mmc)8 mmd)5 mmCorrect answer is option 'A'. Can you explain this answer?
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A tension member of square cross-section of side 10 mm and Young’s modulus E is to be replaced by another member of square cross-section of same length but Young’s modulus E/2. The side of the new square cross-section, required to maintain the same elongation under the same load, is nearlya)14 mmb)17 mmc)8 mmd)5 mmCorrect answer is option 'A'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about A tension member of square cross-section of side 10 mm and Young’s modulus E is to be replaced by another member of square cross-section of same length but Young’s modulus E/2. The side of the new square cross-section, required to maintain the same elongation under the same load, is nearlya)14 mmb)17 mmc)8 mmd)5 mmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A tension member of square cross-section of side 10 mm and Young’s modulus E is to be replaced by another member of square cross-section of same length but Young’s modulus E/2. The side of the new square cross-section, required to maintain the same elongation under the same load, is nearlya)14 mmb)17 mmc)8 mmd)5 mmCorrect answer is option 'A'. Can you explain this answer?.
A tension member of square cross-section of side 10 mm and Young’s modulus E is to be replaced by another member of square cross-section of same length but Young’s modulus E/2. The side of the new square cross-section, required to maintain the same elongation under the same load, is nearlya)14 mmb)17 mmc)8 mmd)5 mmCorrect answer is option 'A'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about A tension member of square cross-section of side 10 mm and Young’s modulus E is to be replaced by another member of square cross-section of same length but Young’s modulus E/2. The side of the new square cross-section, required to maintain the same elongation under the same load, is nearlya)14 mmb)17 mmc)8 mmd)5 mmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A tension member of square cross-section of side 10 mm and Young’s modulus E is to be replaced by another member of square cross-section of same length but Young’s modulus E/2. The side of the new square cross-section, required to maintain the same elongation under the same load, is nearlya)14 mmb)17 mmc)8 mmd)5 mmCorrect answer is option 'A'. Can you explain this answer?.
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