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The outside diameter of a hollow shaft is twice its inside diameter. The ratio of its torque carrying capacity to that of a solid shaft of the same material and the same outside diameter is
- a)15/16
- b)3/4
- c)1/2
- d)3/16
Correct answer is option 'A'. Can you explain this answer?
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The outside diameter of a hollow shaft is twice its inside diameter. T...
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Given: Outside diameter of a hollow shaft = 2 x Inside diameter of a hollow shaft
Let the inside diameter of the hollow shaft be 'd' mm. Therefore, the outside diameter of the hollow shaft is 2d mm.
The area of the hollow shaft can be calculated as follows:
- Area of the outside diameter = π/4 x (2d)^2 = 2πd^2
- Area of the inside diameter = π/4 x d^2
- Area of the hollow shaft = π/4 x (2d)^2 - π/4 x d^2 = 3/4πd^2
The torque carrying capacity of a shaft is directly proportional to its cross-sectional area. Therefore, the torque carrying capacity of the hollow shaft can be calculated as follows:
- Torque carrying capacity of the hollow shaft = (3/4πd^2) x τ (where τ is the shear stress of the material)
Let the outside diameter of the solid shaft be 'D' mm. Therefore, the area of the solid shaft can be calculated as follows:
- Area of the solid shaft = π/4 x D^2
The torque carrying capacity of the solid shaft can be calculated as follows:
- Torque carrying capacity of the solid shaft = (π/4 x D^2) x τ (where τ is the shear stress of the material)
The ratio of torque carrying capacities of the hollow shaft and the solid shaft can be calculated as follows:
- Ratio = (3/4πd^2 x τ) / (π/4 x D^2 x τ) = (3/4d^2) / D^2 = 15/16 (since D = 2d)
Therefore, the correct answer is option 'A' (15/16).
Let the inside diameter of the hollow shaft be 'd' mm. Therefore, the outside diameter of the hollow shaft is 2d mm.
The area of the hollow shaft can be calculated as follows:
- Area of the outside diameter = π/4 x (2d)^2 = 2πd^2
- Area of the inside diameter = π/4 x d^2
- Area of the hollow shaft = π/4 x (2d)^2 - π/4 x d^2 = 3/4πd^2
The torque carrying capacity of a shaft is directly proportional to its cross-sectional area. Therefore, the torque carrying capacity of the hollow shaft can be calculated as follows:
- Torque carrying capacity of the hollow shaft = (3/4πd^2) x τ (where τ is the shear stress of the material)
Let the outside diameter of the solid shaft be 'D' mm. Therefore, the area of the solid shaft can be calculated as follows:
- Area of the solid shaft = π/4 x D^2
The torque carrying capacity of the solid shaft can be calculated as follows:
- Torque carrying capacity of the solid shaft = (π/4 x D^2) x τ (where τ is the shear stress of the material)
The ratio of torque carrying capacities of the hollow shaft and the solid shaft can be calculated as follows:
- Ratio = (3/4πd^2 x τ) / (π/4 x D^2 x τ) = (3/4d^2) / D^2 = 15/16 (since D = 2d)
Therefore, the correct answer is option 'A' (15/16).
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The outside diameter of a hollow shaft is twice its inside diameter. The ratio of its torque carrying capacity to that of a solid shaft of the same material and the same outside diameter isa)15/16b)3/4c)1/2d)3/16Correct answer is option 'A'. Can you explain this answer?
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The outside diameter of a hollow shaft is twice its inside diameter. The ratio of its torque carrying capacity to that of a solid shaft of the same material and the same outside diameter isa)15/16b)3/4c)1/2d)3/16Correct answer is option 'A'. 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 The outside diameter of a hollow shaft is twice its inside diameter. The ratio of its torque carrying capacity to that of a solid shaft of the same material and the same outside diameter isa)15/16b)3/4c)1/2d)3/16Correct answer is option 'A'. 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 The outside diameter of a hollow shaft is twice its inside diameter. The ratio of its torque carrying capacity to that of a solid shaft of the same material and the same outside diameter isa)15/16b)3/4c)1/2d)3/16Correct answer is option 'A'. Can you explain this answer?.
The outside diameter of a hollow shaft is twice its inside diameter. The ratio of its torque carrying capacity to that of a solid shaft of the same material and the same outside diameter isa)15/16b)3/4c)1/2d)3/16Correct answer is option 'A'. 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 The outside diameter of a hollow shaft is twice its inside diameter. The ratio of its torque carrying capacity to that of a solid shaft of the same material and the same outside diameter isa)15/16b)3/4c)1/2d)3/16Correct answer is option 'A'. 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 The outside diameter of a hollow shaft is twice its inside diameter. The ratio of its torque carrying capacity to that of a solid shaft of the same material and the same outside diameter isa)15/16b)3/4c)1/2d)3/16Correct answer is option 'A'. Can you explain this answer?.
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