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A hollow shaft of inner radius 30 mm and outer radius 50 mm is subjected to a twisting moment. If the shear stress developed at an inner radius of the shaft is 60 N/mm2. What is the maximum shear stress in the shaft?
- a)60 N/mm2
- b)75 N/mm2
- c)100 N/mm2
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A hollow shaft of inner radius 30 mm and outer radius 50 mm is subjec...
As we know, torsional shear stress varies linearly
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= 100 N/mm2
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A hollow shaft of inner radius 30 mm and outer radius 50 mm is subjec...
Understanding Shear Stress in a Hollow Shaft
To determine the maximum shear stress in the hollow shaft, we need to analyze the given parameters.
Given Data:
- Inner radius (r1) = 30 mm
- Outer radius (r2) = 50 mm
- Shear stress at inner radius (τ1) = 60 N/mm²
Shear Stress Distribution:
In a hollow shaft subjected to twisting moments, the shear stress varies linearly from the inner radius to the outer radius. The maximum shear stress occurs at the outer radius.
Calculating Maximum Shear Stress:
1. The shear stress formula for a hollow shaft is:
τ = T * r / J, where:
- T = Twisting moment
- r = Radius at which shear stress is being calculated
- J = Polar moment of inertia
2. The polar moment of inertia for a hollow shaft is given by:
J = (π/32) * (r2^4 - r1^4)
3. Since the shear stress is linearly dependent on the radius, we can deduce that:
τ_max (at outer radius) = τ1 * (r2/r1)
4. Substituting the values:
τ_max = 60 N/mm² * (50 mm / 30 mm) = 60 N/mm² * 1.6667 ≈ 100 N/mm²
Conclusion:
Thus, the maximum shear stress in the shaft is calculated to be approximately 100 N/mm².
Final Answer:
The correct answer is option 'C' – 100 N/mm².
To determine the maximum shear stress in the hollow shaft, we need to analyze the given parameters.
Given Data:
- Inner radius (r1) = 30 mm
- Outer radius (r2) = 50 mm
- Shear stress at inner radius (τ1) = 60 N/mm²
Shear Stress Distribution:
In a hollow shaft subjected to twisting moments, the shear stress varies linearly from the inner radius to the outer radius. The maximum shear stress occurs at the outer radius.
Calculating Maximum Shear Stress:
1. The shear stress formula for a hollow shaft is:
τ = T * r / J, where:
- T = Twisting moment
- r = Radius at which shear stress is being calculated
- J = Polar moment of inertia
2. The polar moment of inertia for a hollow shaft is given by:
J = (π/32) * (r2^4 - r1^4)
3. Since the shear stress is linearly dependent on the radius, we can deduce that:
τ_max (at outer radius) = τ1 * (r2/r1)
4. Substituting the values:
τ_max = 60 N/mm² * (50 mm / 30 mm) = 60 N/mm² * 1.6667 ≈ 100 N/mm²
Conclusion:
Thus, the maximum shear stress in the shaft is calculated to be approximately 100 N/mm².
Final Answer:
The correct answer is option 'C' – 100 N/mm².
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A hollow shaft of inner radius 30 mm and outer radius 50 mm is subjected to a twisting moment. If the shear stress developed at an inner radius of the shaft is 60 N/mm2. What is the maximum shear stress in the shaft?a)60 N/mm2b)75 N/mm2c)100 N/mm2d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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A hollow shaft of inner radius 30 mm and outer radius 50 mm is subjected to a twisting moment. If the shear stress developed at an inner radius of the shaft is 60 N/mm2. What is the maximum shear stress in the shaft?a)60 N/mm2b)75 N/mm2c)100 N/mm2d)None of theseCorrect answer is option 'C'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about A hollow shaft of inner radius 30 mm and outer radius 50 mm is subjected to a twisting moment. If the shear stress developed at an inner radius of the shaft is 60 N/mm2. What is the maximum shear stress in the shaft?a)60 N/mm2b)75 N/mm2c)100 N/mm2d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hollow shaft of inner radius 30 mm and outer radius 50 mm is subjected to a twisting moment. If the shear stress developed at an inner radius of the shaft is 60 N/mm2. What is the maximum shear stress in the shaft?a)60 N/mm2b)75 N/mm2c)100 N/mm2d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
A hollow shaft of inner radius 30 mm and outer radius 50 mm is subjected to a twisting moment. If the shear stress developed at an inner radius of the shaft is 60 N/mm2. What is the maximum shear stress in the shaft?a)60 N/mm2b)75 N/mm2c)100 N/mm2d)None of theseCorrect answer is option 'C'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about A hollow shaft of inner radius 30 mm and outer radius 50 mm is subjected to a twisting moment. If the shear stress developed at an inner radius of the shaft is 60 N/mm2. What is the maximum shear stress in the shaft?a)60 N/mm2b)75 N/mm2c)100 N/mm2d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hollow shaft of inner radius 30 mm and outer radius 50 mm is subjected to a twisting moment. If the shear stress developed at an inner radius of the shaft is 60 N/mm2. What is the maximum shear stress in the shaft?a)60 N/mm2b)75 N/mm2c)100 N/mm2d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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A hollow shaft of inner radius 30 mm and outer radius 50 mm is subjected to a twisting moment. If the shear stress developed at an inner radius of the shaft is 60 N/mm2. What is the maximum shear stress in the shaft?a)60 N/mm2b)75 N/mm2c)100 N/mm2d)None of theseCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A hollow shaft of inner radius 30 mm and outer radius 50 mm is subjected to a twisting moment. If the shear stress developed at an inner radius of the shaft is 60 N/mm2. What is the maximum shear stress in the shaft?a)60 N/mm2b)75 N/mm2c)100 N/mm2d)None of theseCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A hollow shaft of inner radius 30 mm and outer radius 50 mm is subjected to a twisting moment. If the shear stress developed at an inner radius of the shaft is 60 N/mm2. What is the maximum shear stress in the shaft?a)60 N/mm2b)75 N/mm2c)100 N/mm2d)None of theseCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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