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Two bars of different materials are of the same size and are subjected to same tensile forces. If the bars have unit elongations in the ratio of 3 : 8, then the ratio of moduli of elasticity of the two materials is:
  • a)
    7 : 4
  • b)
    3 : 8
  • c)
    8 : 3
  • d)
    64 : 9
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Two bars of different materials are of the same size and are subjected...
Solution:

Given,

Unit elongation of bar A to bar B = 3 : 8

Let,

A = Area of cross-section of the bar

L = Length of the bar

F = Tensile force applied on the bar

σA = Stress developed in bar A

σB = Stress developed in bar B

Ea = Modulus of elasticity of material A

Eb = Modulus of elasticity of material B

Formula used:

Stress = Force / Area

Unit elongation = Elongation / Original length

Stress = Modulus of elasticity × Strain

Calculation:

Let us assume that the original length of both bars is L.

Then, the elongation produced in bar A and bar B is 3L and 8L respectively.

According to the question,

Unit elongation of bar A to bar B = 3 : 8

∴ 3L / L = Ea / Eb

∴ Ea / Eb = 3 / 8

Stress developed in bar A = F / A

Stress developed in bar B = F / A

From the formula of stress,

Stress = Modulus of elasticity × Strain

∴ σA / Ea = 3L / L

∴ σA = 3Ea

Similarly,

σB / Eb = 8L / L

∴ σB = 8Eb

Now,

σA / σB = F / A × Eb / F × A / Ea

∴ σA / σB = Ea / Eb

From the above calculation,

Ea / Eb = 3 / 8

∴ σA / σB = 3 / 8

Therefore, the ratio of moduli of elasticity of the two materials is 8 : 3.

Hence, the correct option is (c) 8 : 3.
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Community Answer
Two bars of different materials are of the same size and are subjected...
Pl/AE1=pl/AE2=3:8
E2/E1=3/8
E1/E2=8/3
E1/E2=8:3
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Two bars of different materials are of the same size and are subjected to same tensile forces. If the bars have unit elongations in the ratio of 3 : 8, then the ratio of moduli of elasticity of the two materials is:a)7 : 4b)3 : 8c)8 : 3d)64 : 9Correct answer is option 'C'. Can you explain this answer?
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Two bars of different materials are of the same size and are subjected to same tensile forces. If the bars have unit elongations in the ratio of 3 : 8, then the ratio of moduli of elasticity of the two materials is:a)7 : 4b)3 : 8c)8 : 3d)64 : 9Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Two bars of different materials are of the same size and are subjected to same tensile forces. If the bars have unit elongations in the ratio of 3 : 8, then the ratio of moduli of elasticity of the two materials is:a)7 : 4b)3 : 8c)8 : 3d)64 : 9Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two bars of different materials are of the same size and are subjected to same tensile forces. If the bars have unit elongations in the ratio of 3 : 8, then the ratio of moduli of elasticity of the two materials is:a)7 : 4b)3 : 8c)8 : 3d)64 : 9Correct answer is option 'C'. Can you explain this answer?.
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