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Two tapering bars of the same material are subjected to a tensile load P. The lengths of both the bars are the same. The larger diameter of each of the bars is D. The diameter of the bar A at its smaller end is D/2 and that of the bar b is D/3. What is the ratio of elongation of the bar A to that of the bar B?
- a)3:2
- b)2:3
- c)4:9
- d)1:3
Correct answer is option 'B'. Can you explain this answer?
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Two tapering bars of the same material are subjected to a tensile loa...
Elongation of bar A
Elongation of bar B
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Two tapering bars of the same material are subjected to a tensile loa...
To determine the ratio of elongation of bar A to bar B, let's consider the properties of the bars and analyze the behavior under tensile load.
Given:
- Both bars have the same length.
- Bar A has a larger diameter at its larger end (D) and a smaller diameter at its smaller end (D/2).
- Bar B has a larger diameter at its larger end (D) and a smaller diameter at its smaller end (D/3).
Analysis:
1. Cross-sectional Area:
- The cross-sectional area of bar A varies linearly from D²/4 to (D/2)²/4.
- The cross-sectional area of bar B varies linearly from D²/4 to (D/3)²/4.
2. Stress:
- The stress experienced by both bars is given by the formula: Stress = Load / Area.
- As the load is the same for both bars (P), the stress will be inversely proportional to the cross-sectional area.
3. Strain:
- Strain is defined as the ratio of the change in length to the original length.
- The elongation of a bar is directly proportional to the strain, given by the formula: Strain = Stress / Young's Modulus.
4. Young's Modulus:
- Young's Modulus is a material property that describes its stiffness or resistance to deformation under load.
- Since both bars are made of the same material, their Young's Modulus values are equal.
Calculation:
1. Elongation of Bar A:
- Since the stress is inversely proportional to the cross-sectional area, the strain in bar A will be inversely proportional to the cross-sectional area.
- The strain in bar A will be (D/2)²/4 / D²/4 = (D/2)² / D² = 1/4.
- Therefore, the elongation of bar A will be 1/4 times the elongation of bar B.
2. Elongation of Bar B:
- The strain in bar B will be (D/3)²/4 / D²/4 = (D/3)² / D² = 1/9.
Ratio of Elongation:
- Elongation of bar A : Elongation of bar B = 1/4 : 1/9
- Simplifying the ratio, we get 9/4 : 1
- Therefore, the ratio of elongation of bar A to bar B is 9:4, which is equivalent to 2:3 (approximately).
Therefore, the correct answer is option 'B' - 2:3.
Given:
- Both bars have the same length.
- Bar A has a larger diameter at its larger end (D) and a smaller diameter at its smaller end (D/2).
- Bar B has a larger diameter at its larger end (D) and a smaller diameter at its smaller end (D/3).
Analysis:
1. Cross-sectional Area:
- The cross-sectional area of bar A varies linearly from D²/4 to (D/2)²/4.
- The cross-sectional area of bar B varies linearly from D²/4 to (D/3)²/4.
2. Stress:
- The stress experienced by both bars is given by the formula: Stress = Load / Area.
- As the load is the same for both bars (P), the stress will be inversely proportional to the cross-sectional area.
3. Strain:
- Strain is defined as the ratio of the change in length to the original length.
- The elongation of a bar is directly proportional to the strain, given by the formula: Strain = Stress / Young's Modulus.
4. Young's Modulus:
- Young's Modulus is a material property that describes its stiffness or resistance to deformation under load.
- Since both bars are made of the same material, their Young's Modulus values are equal.
Calculation:
1. Elongation of Bar A:
- Since the stress is inversely proportional to the cross-sectional area, the strain in bar A will be inversely proportional to the cross-sectional area.
- The strain in bar A will be (D/2)²/4 / D²/4 = (D/2)² / D² = 1/4.
- Therefore, the elongation of bar A will be 1/4 times the elongation of bar B.
2. Elongation of Bar B:
- The strain in bar B will be (D/3)²/4 / D²/4 = (D/3)² / D² = 1/9.
Ratio of Elongation:
- Elongation of bar A : Elongation of bar B = 1/4 : 1/9
- Simplifying the ratio, we get 9/4 : 1
- Therefore, the ratio of elongation of bar A to bar B is 9:4, which is equivalent to 2:3 (approximately).
Therefore, the correct answer is option 'B' - 2:3.
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Two tapering bars of the same material are subjected to a tensile load P. The lengths of both the bars are the same. The larger diameter of each of the bars is D. The diameter of the bar A at its smaller end is D/2 and that of the bar b is D/3. What is the ratio of elongation of the bar A to that of the bar B?a) 3:2b) 2:3c) 4:9d) 1:3Correct answer is option 'B'. Can you explain this answer?
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Two tapering bars of the same material are subjected to a tensile load P. The lengths of both the bars are the same. The larger diameter of each of the bars is D. The diameter of the bar A at its smaller end is D/2 and that of the bar b is D/3. What is the ratio of elongation of the bar A to that of the bar B?a) 3:2b) 2:3c) 4:9d) 1:3Correct answer is option 'B'. 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 tapering bars of the same material are subjected to a tensile load P. The lengths of both the bars are the same. The larger diameter of each of the bars is D. The diameter of the bar A at its smaller end is D/2 and that of the bar b is D/3. What is the ratio of elongation of the bar A to that of the bar B?a) 3:2b) 2:3c) 4:9d) 1:3Correct answer is option 'B'. 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 tapering bars of the same material are subjected to a tensile load P. The lengths of both the bars are the same. The larger diameter of each of the bars is D. The diameter of the bar A at its smaller end is D/2 and that of the bar b is D/3. What is the ratio of elongation of the bar A to that of the bar B?a) 3:2b) 2:3c) 4:9d) 1:3Correct answer is option 'B'. Can you explain this answer?.
Two tapering bars of the same material are subjected to a tensile load P. The lengths of both the bars are the same. The larger diameter of each of the bars is D. The diameter of the bar A at its smaller end is D/2 and that of the bar b is D/3. What is the ratio of elongation of the bar A to that of the bar B?a) 3:2b) 2:3c) 4:9d) 1:3Correct answer is option 'B'. 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 tapering bars of the same material are subjected to a tensile load P. The lengths of both the bars are the same. The larger diameter of each of the bars is D. The diameter of the bar A at its smaller end is D/2 and that of the bar b is D/3. What is the ratio of elongation of the bar A to that of the bar B?a) 3:2b) 2:3c) 4:9d) 1:3Correct answer is option 'B'. 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 tapering bars of the same material are subjected to a tensile load P. The lengths of both the bars are the same. The larger diameter of each of the bars is D. The diameter of the bar A at its smaller end is D/2 and that of the bar b is D/3. What is the ratio of elongation of the bar A to that of the bar B?a) 3:2b) 2:3c) 4:9d) 1:3Correct answer is option 'B'. Can you explain this answer?.
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Two tapering bars of the same material are subjected to a tensile load P. The lengths of both the bars are the same. The larger diameter of each of the bars is D. The diameter of the bar A at its smaller end is D/2 and that of the bar b is D/3. What is the ratio of elongation of the bar A to that of the bar B?a) 3:2b) 2:3c) 4:9d) 1:3Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Two tapering bars of the same material are subjected to a tensile load P. The lengths of both the bars are the same. The larger diameter of each of the bars is D. The diameter of the bar A at its smaller end is D/2 and that of the bar b is D/3. What is the ratio of elongation of the bar A to that of the bar B?a) 3:2b) 2:3c) 4:9d) 1:3Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Two tapering bars of the same material are subjected to a tensile load P. The lengths of both the bars are the same. The larger diameter of each of the bars is D. The diameter of the bar A at its smaller end is D/2 and that of the bar b is D/3. What is the ratio of elongation of the bar A to that of the bar B?a) 3:2b) 2:3c) 4:9d) 1:3Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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