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The outside diameter of a hollow shaft that is twice its inside diameter the ratio of its torquecarrying 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)1/16
Correct answer is option 'A'. Can you explain this answer?
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The outside diameter of a hollow shaft that is twice its inside diamet...
Calculation of Outside and Inside Diameter of Hollow Shaft:
Let the inside diameter of the hollow shaft be 'd' and the outside diameter be '2d'
Ratio of Torque-carrying capacity of the Hollow shaft to the Solid shaft:
The torque-carrying capacity of the shaft is proportional to the fourth power of the shaft diameter.
Hence, the torque-carrying capacity of the hollow shaft can be calculated as follows:
Torque-carrying capacity of the hollow shaft = (π/16) × (D^4 - d^4)
where D is the outside diameter of the hollow shaft and d is the inside diameter of the hollow shaft.
Similarly, the torque-carrying capacity of the solid shaft can be calculated as follows:
Torque-carrying capacity of the solid shaft = (π/16) × D^4
Ratio of torque-carrying capacity = (D^4 - d^4) / D^4
= 1 - (d/D)^4
Given, D = 2d
Hence, (d/D) = 1/2
∴ Ratio of torque-carrying capacity = 1 - (1/2)^4
= 1 - 1/16
= 15/16
Therefore, the ratio of torque-carrying capacity of the hollow shaft to that of the solid shaft is 15/16.
Let the inside diameter of the hollow shaft be 'd' and the outside diameter be '2d'
Ratio of Torque-carrying capacity of the Hollow shaft to the Solid shaft:
The torque-carrying capacity of the shaft is proportional to the fourth power of the shaft diameter.
Hence, the torque-carrying capacity of the hollow shaft can be calculated as follows:
Torque-carrying capacity of the hollow shaft = (π/16) × (D^4 - d^4)
where D is the outside diameter of the hollow shaft and d is the inside diameter of the hollow shaft.
Similarly, the torque-carrying capacity of the solid shaft can be calculated as follows:
Torque-carrying capacity of the solid shaft = (π/16) × D^4
Ratio of torque-carrying capacity = (D^4 - d^4) / D^4
= 1 - (d/D)^4
Given, D = 2d
Hence, (d/D) = 1/2
∴ Ratio of torque-carrying capacity = 1 - (1/2)^4
= 1 - 1/16
= 15/16
Therefore, the ratio of torque-carrying capacity of the hollow shaft to that of the solid shaft is 15/16.
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The outside diameter of a hollow shaft that is twice its inside diameter the ratio of its torquecarrying capacity to that of a solid shaft of the same material and the same outside diameter isa)15/16b)3/4c)1/2d)1/16Correct answer is option 'A'. Can you explain this answer?
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