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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?
Verified Answer
A tension member of square cross-section of side 10 mm and Young’s mo...
Member 1,
Area(A1) = 10 x 10mm2 = 100mm2
E1 = E
Member2,
E2 = E/2
A2 =?
Given , P1 = P2: and L1 = L2 and δ1 = δ2
If a is the length of the side of square
a2 = 200
a = 14.142 mm
This question is part of UPSC exam. View all Mechanical Engineering courses
Most Upvoted Answer
A tension member of square cross-section of side 10 mm and Young’s mo...
To find the side of the new square cross-section required to maintain the same elongation under the same load, we can use the concept of stress and strain in tension members.
Stress is defined as the force applied per unit area of the cross-section, and strain is defined as the change in length per unit length of the member.
Given:
Side of the original square cross-section (S1) = 10 mm
Young's modulus of the original member (E1) = E
Young's modulus of the new member (E2) = E/2
We know that stress is directly proportional to strain, according to Hooke's Law:
Stress = E * Strain
Since we want to maintain the same elongation under the same load, the strain in both members should be the same.
Let's assume the side of the new square cross-section is S2.
Calculating the stress in the original member:
Stress1 = Load / Area1
Stress1 = Load / (S1 * S1)
Calculating the strain in the original member:
Strain1 = Change in length / Original length
Strain1 = Elongation / Original length
Calculating the stress in the new member:
Stress2 = Load / Area2
Stress2 = Load / (S2 * S2)
Calculating the strain in the new member:
Strain2 = Change in length / Original length
Strain2 = Elongation / Original length
Since the strain in both members should be the same:
Strain1 = Strain2
Elongation / Original length = Elongation / Original length
Substituting the values:
Elongation / (S1 * S1) = Elongation / (S2 * S2)
Simplifying the equation:
S2 * S2 = S1 * S1
Taking the square root of both sides:
S2 = S1
Therefore, the side of the new square cross-section required to maintain the same elongation under the same load is equal to the side of the original square cross-section.
Hence, the answer is option 'A' - 14 mm.
Stress is defined as the force applied per unit area of the cross-section, and strain is defined as the change in length per unit length of the member.
Given:
Side of the original square cross-section (S1) = 10 mm
Young's modulus of the original member (E1) = E
Young's modulus of the new member (E2) = E/2
We know that stress is directly proportional to strain, according to Hooke's Law:
Stress = E * Strain
Since we want to maintain the same elongation under the same load, the strain in both members should be the same.
Let's assume the side of the new square cross-section is S2.
Calculating the stress in the original member:
Stress1 = Load / Area1
Stress1 = Load / (S1 * S1)
Calculating the strain in the original member:
Strain1 = Change in length / Original length
Strain1 = Elongation / Original length
Calculating the stress in the new member:
Stress2 = Load / Area2
Stress2 = Load / (S2 * S2)
Calculating the strain in the new member:
Strain2 = Change in length / Original length
Strain2 = Elongation / Original length
Since the strain in both members should be the same:
Strain1 = Strain2
Elongation / Original length = Elongation / Original length
Substituting the values:
Elongation / (S1 * S1) = Elongation / (S2 * S2)
Simplifying the equation:
S2 * S2 = S1 * S1
Taking the square root of both sides:
S2 = S1
Therefore, the side of the new square cross-section required to maintain the same elongation under the same load is equal to the side of the original square cross-section.
Hence, the answer is option 'A' - 14 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?
Question Description
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 Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering 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 Mechanical Engineering 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 Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering 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 Mechanical Engineering 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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