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A circular shaft of diameter D is subjected to a torque T. The maximum shear stress of the shaft will be-
- a)proportional to (D3)
- b)proportional to (D4)
- c)inversely proportional to (D3)
- d)inversely proportional to (D4)
Correct answer is option 'C'. Can you explain this answer?
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A circular shaft of diameter D is subjected to a torque T. The maximu...
tmax is inversely proportional to (D3)
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A circular shaft of diameter D is subjected to a torque T. The maximu...
Explanation:
Shear Stress in a Circular Shaft:
- When a torque is applied to a circular shaft, it creates shear stress within the material.
- The formula for shear stress in a circular shaft is τ = Tc / J, where T is the torque, c is the radial distance from the center of the shaft to the outer surface, and J is the polar moment of inertia.
Relationship with Diameter:
- The polar moment of inertia, J, for a circular shaft is directly proportional to the fourth power of the diameter, D⁴ (J ∝ D⁴).
- Therefore, the shear stress (τ) is inversely proportional to the diameter cubed, as J increases with the fourth power of diameter while shear stress decreases with the third power of diameter.
- This relationship is represented by the formula τ ∝ 1/D³.
Conclusion:
- The maximum shear stress in a circular shaft subjected to a torque is inversely proportional to the cube of the diameter, making option 'C' the correct answer.
Shear Stress in a Circular Shaft:
- When a torque is applied to a circular shaft, it creates shear stress within the material.
- The formula for shear stress in a circular shaft is τ = Tc / J, where T is the torque, c is the radial distance from the center of the shaft to the outer surface, and J is the polar moment of inertia.
Relationship with Diameter:
- The polar moment of inertia, J, for a circular shaft is directly proportional to the fourth power of the diameter, D⁴ (J ∝ D⁴).
- Therefore, the shear stress (τ) is inversely proportional to the diameter cubed, as J increases with the fourth power of diameter while shear stress decreases with the third power of diameter.
- This relationship is represented by the formula τ ∝ 1/D³.
Conclusion:
- The maximum shear stress in a circular shaft subjected to a torque is inversely proportional to the cube of the diameter, making option 'C' the correct answer.
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A circular shaft of diameter D is subjected to a torque T. The maximum shear stress of the shaft will be-a)proportional to (D3)b)proportional to (D4)c)inversely proportional to (D3)d)inversely proportional to (D4)Correct answer is option 'C'. Can you explain this answer?
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A circular shaft of diameter D is subjected to a torque T. The maximum shear stress of the shaft will be-a)proportional to (D3)b)proportional to (D4)c)inversely proportional to (D3)d)inversely proportional to (D4)Correct 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 circular shaft of diameter D is subjected to a torque T. The maximum shear stress of the shaft will be-a)proportional to (D3)b)proportional to (D4)c)inversely proportional to (D3)d)inversely proportional to (D4)Correct 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 circular shaft of diameter D is subjected to a torque T. The maximum shear stress of the shaft will be-a)proportional to (D3)b)proportional to (D4)c)inversely proportional to (D3)d)inversely proportional to (D4)Correct answer is option 'C'. Can you explain this answer?.
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