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Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 GPa. The other rod is made out of cast iron having the modulus of elasticity of 100 GPa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct?
- a)Both rods elongate by the same amount
- b)Mild steel rod elongates more than the cast iron rod
- c)Cast iron rod elongates more than the mild steel rod
- d)As the stresses are equal strains are also equal in both the rods
Correct answer is 'C'. Can you explain this answer?
Verified Answer
Two identical circular rods of same diameter and same length are subje...
Stress are equal in both materials
Length of the both rods are same
From equation of Modulus of elasticity = stress / strain = (force * length) / (area * change in length)
here force, length and area remain same so modulus of elasticity are directly proportional to change in length
So
For Mild steel 206 ≈ 1 / change in length
change in length for mild steel ≈ 1 / 206 ≈ 0.0048
For Cast iron 100 ≈ 1 / change in length
change in length for Cast iron ≈ 1 / 100 ≈ 0.01
so (elongation) change in length are higher in Cast iron
This question is part of UPSC exam. View all Mechanical Engineering courses
Most Upvoted Answer
Two identical circular rods of same diameter and same length are subje...
Deflection = wl/AE . hence 1/E is compared as all other elements are same. 1/100 > 1/206 . that means the deflection of cast iron is more than mild steel.
Community Answer
Two identical circular rods of same diameter and same length are subje...
Explanation:
When a material is subjected to an axial tensile force, it undergoes deformation in the form of elongation. The amount of elongation is determined by the material's modulus of elasticity and the magnitude of the force applied.
Modulus of Elasticity:
The modulus of elasticity, also known as Young's modulus, is a material property that describes its stiffness or ability to resist deformation under an applied force. It represents the ratio of stress to strain within the proportional limit of the material.
In this question, the mild steel rod has a modulus of elasticity of 206 GPa, while the cast iron rod has a modulus of elasticity of 100 GPa. Since the modulus of elasticity is higher for mild steel, it indicates that mild steel is stiffer and more resistant to deformation compared to cast iron.
Stress and Strain:
When an axial force is applied to a rod, it creates a uniform stress throughout the cross-section of the rod. The stress is calculated by dividing the applied force by the cross-sectional area of the rod.
Since the rods have the same diameter, the cross-sectional areas of the rods are the same. Therefore, the stress developed in both rods will be equal.
However, the strain developed in each rod will be different due to the difference in their modulus of elasticity. Strain is calculated by dividing the change in length of the rod by its original length.
Elongation:
Since the stress is equal in both rods, but the modulus of elasticity is higher for mild steel, it means that the strain developed in mild steel will be less compared to cast iron for the same magnitude of force.
As strain is directly proportional to elongation, it implies that the mild steel rod will experience less elongation compared to the cast iron rod.
Therefore, the correct observation is that the cast iron rod elongates more than the mild steel rod when subjected to the same magnitude of axial tensile force.
When a material is subjected to an axial tensile force, it undergoes deformation in the form of elongation. The amount of elongation is determined by the material's modulus of elasticity and the magnitude of the force applied.
Modulus of Elasticity:
The modulus of elasticity, also known as Young's modulus, is a material property that describes its stiffness or ability to resist deformation under an applied force. It represents the ratio of stress to strain within the proportional limit of the material.
In this question, the mild steel rod has a modulus of elasticity of 206 GPa, while the cast iron rod has a modulus of elasticity of 100 GPa. Since the modulus of elasticity is higher for mild steel, it indicates that mild steel is stiffer and more resistant to deformation compared to cast iron.
Stress and Strain:
When an axial force is applied to a rod, it creates a uniform stress throughout the cross-section of the rod. The stress is calculated by dividing the applied force by the cross-sectional area of the rod.
Since the rods have the same diameter, the cross-sectional areas of the rods are the same. Therefore, the stress developed in both rods will be equal.
However, the strain developed in each rod will be different due to the difference in their modulus of elasticity. Strain is calculated by dividing the change in length of the rod by its original length.
Elongation:
Since the stress is equal in both rods, but the modulus of elasticity is higher for mild steel, it means that the strain developed in mild steel will be less compared to cast iron for the same magnitude of force.
As strain is directly proportional to elongation, it implies that the mild steel rod will experience less elongation compared to the cast iron rod.
Therefore, the correct observation is that the cast iron rod elongates more than the mild steel rod when subjected to the same magnitude of axial tensile force.
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Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 GPa. The other rod is made out of cast iron having the modulus of elasticity of 100 GPa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct?a)Both rods elongate by the same amountb)Mild steel rod elongates more than the cast iron rodc)Cast iron rod elongates more than the mild steel rodd)As the stresses are equal strains are also equal in both the rodsCorrect answer is 'C'. Can you explain this answer?
Question Description
Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 GPa. The other rod is made out of cast iron having the modulus of elasticity of 100 GPa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct?a)Both rods elongate by the same amountb)Mild steel rod elongates more than the cast iron rodc)Cast iron rod elongates more than the mild steel rodd)As the stresses are equal strains are also equal in both the rodsCorrect answer is 'C'. 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 Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 GPa. The other rod is made out of cast iron having the modulus of elasticity of 100 GPa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct?a)Both rods elongate by the same amountb)Mild steel rod elongates more than the cast iron rodc)Cast iron rod elongates more than the mild steel rodd)As the stresses are equal strains are also equal in both the rodsCorrect answer is 'C'. 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 Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 GPa. The other rod is made out of cast iron having the modulus of elasticity of 100 GPa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct?a)Both rods elongate by the same amountb)Mild steel rod elongates more than the cast iron rodc)Cast iron rod elongates more than the mild steel rodd)As the stresses are equal strains are also equal in both the rodsCorrect answer is 'C'. Can you explain this answer?.
Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 GPa. The other rod is made out of cast iron having the modulus of elasticity of 100 GPa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct?a)Both rods elongate by the same amountb)Mild steel rod elongates more than the cast iron rodc)Cast iron rod elongates more than the mild steel rodd)As the stresses are equal strains are also equal in both the rodsCorrect answer is 'C'. 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 Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 GPa. The other rod is made out of cast iron having the modulus of elasticity of 100 GPa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct?a)Both rods elongate by the same amountb)Mild steel rod elongates more than the cast iron rodc)Cast iron rod elongates more than the mild steel rodd)As the stresses are equal strains are also equal in both the rodsCorrect answer is 'C'. 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 Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 GPa. The other rod is made out of cast iron having the modulus of elasticity of 100 GPa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct?a)Both rods elongate by the same amountb)Mild steel rod elongates more than the cast iron rodc)Cast iron rod elongates more than the mild steel rodd)As the stresses are equal strains are also equal in both the rodsCorrect answer is 'C'. Can you explain this answer?.
Solutions for Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 GPa. The other rod is made out of cast iron having the modulus of elasticity of 100 GPa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct?a)Both rods elongate by the same amountb)Mild steel rod elongates more than the cast iron rodc)Cast iron rod elongates more than the mild steel rodd)As the stresses are equal strains are also equal in both the rodsCorrect answer is 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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Here you can find the meaning of Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 GPa. The other rod is made out of cast iron having the modulus of elasticity of 100 GPa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct?a)Both rods elongate by the same amountb)Mild steel rod elongates more than the cast iron rodc)Cast iron rod elongates more than the mild steel rodd)As the stresses are equal strains are also equal in both the rodsCorrect answer is 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 GPa. The other rod is made out of cast iron having the modulus of elasticity of 100 GPa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct?a)Both rods elongate by the same amountb)Mild steel rod elongates more than the cast iron rodc)Cast iron rod elongates more than the mild steel rodd)As the stresses are equal strains are also equal in both the rodsCorrect answer is 'C'. Can you explain this answer?, a detailed solution for Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 GPa. The other rod is made out of cast iron having the modulus of elasticity of 100 GPa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct?a)Both rods elongate by the same amountb)Mild steel rod elongates more than the cast iron rodc)Cast iron rod elongates more than the mild steel rodd)As the stresses are equal strains are also equal in both the rodsCorrect answer is 'C'. Can you explain this answer? has been provided alongside types of Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 GPa. The other rod is made out of cast iron having the modulus of elasticity of 100 GPa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct?a)Both rods elongate by the same amountb)Mild steel rod elongates more than the cast iron rodc)Cast iron rod elongates more than the mild steel rodd)As the stresses are equal strains are also equal in both the rodsCorrect answer is 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 GPa. The other rod is made out of cast iron having the modulus of elasticity of 100 GPa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct?a)Both rods elongate by the same amountb)Mild steel rod elongates more than the cast iron rodc)Cast iron rod elongates more than the mild steel rodd)As the stresses are equal strains are also equal in both the rodsCorrect answer is 'C'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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