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A solid shaft of diameter 100 mm, length 1000 mm is subjected to a twisting moment 'T‟ The maximum shear stress developed in the shaft is 60 N/mm2. A hole of 50 mm diameter is now drilled throughout the length of the shaft. To develop a maximum shear stress of 60 N/mm2 in the hollow shaft, the torque 'T‟ must be reduced by: 
  • a)
    T/4
  • b)
    T/8
  • c)
    T/12
  • d)
    T/16
Correct answer is option 'D'. Can you explain this answer?
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Shaft with a Hole: Reduction in Torque

Given:
Diameter of the solid shaft (before drilling) = 100 mm
Length of the shaft = 1000 mm
Maximum shear stress developed in the solid shaft = 60 N/mm²
Diameter of the hole drilled = 50 mm

To find:
The reduction in torque (T) required to develop a maximum shear stress of 60 N/mm² in the hollow shaft.

Assumptions:
1. The material of the shaft is homogeneous and isotropic.
2. The shaft is under pure torsion.
3. The hollow shaft has a constant thickness throughout its length.

Analysis:
1. Solid Shaft:
- The maximum shear stress (τ) in a solid shaft can be calculated using the formula:
τ = 16T / (πd³),
where T is the torque and d is the diameter of the solid shaft.

- Substituting the given values:
60 = 16T / (π * 100³)

- Solving for T:
T = (60 * π * 100³) / 16

2. Hollow Shaft:
- The maximum shear stress (τ) in a hollow shaft can be calculated using the formula:
τ = 16T / (π(D⁴ - d⁴)),
where D is the outer diameter and d is the inner diameter of the hollow shaft.

- We need to find the reduction in torque (T') to develop the same maximum shear stress of 60 N/mm² in the hollow shaft.

- Substituting the given values:
60 = 16T' / (π * (100⁴ - 50⁴))

- Solving for T':
T' = (60 * π * (100⁴ - 50⁴)) / 16

- The reduction in torque is given by:
Reduction in torque (ΔT) = T - T'
= (60 * π * 100³) / 16 - (60 * π * (100⁴ - 50⁴)) / 16
= (60 * π * (100³ - (100⁴ - 50⁴))) / 16
= (60 * π * (100³ - 100⁴ + 50⁴)) / 16
= (60 * π * (100³ - 100⁴ + 50⁴)) / 16
= (60 * π * (100³ + 100⁴ - 50⁴)) / 16
= (60 * π * (100³(1 + 10) - 50⁴)) / 16
= (60 * π * 100³(11 - 50⁴)) / 16
= (60 * π * 100³(11 - (100⁴ - 2 * 100² * 50² + 50⁴))) / 16
= (60 * π * 100³(11 - 100⁴ + 2 * 100² * 50² - 50⁴)) / 16
= (60 * π * 100³(-100⁴ + 2 * 100² * 50² + 11 - 50
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A solid shaft of diameter 100 mm, length 1000 mm is subjected to a twisting moment 'T‟ The maximum shear stress developed in the shaft is 60 N/mm2. A hole of 50 mm diameter is now drilled throughout the length of the shaft. To develop a maximum shear stress of 60 N/mm2 in the hollow shaft, the torque 'T‟ must be reduced by:a)T/4b)T/8c)T/12d)T/16Correct answer is option 'D'. Can you explain this answer?
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A solid shaft of diameter 100 mm, length 1000 mm is subjected to a twisting moment 'T‟ The maximum shear stress developed in the shaft is 60 N/mm2. A hole of 50 mm diameter is now drilled throughout the length of the shaft. To develop a maximum shear stress of 60 N/mm2 in the hollow shaft, the torque 'T‟ must be reduced by:a)T/4b)T/8c)T/12d)T/16Correct answer is option 'D'. 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 A solid shaft of diameter 100 mm, length 1000 mm is subjected to a twisting moment 'T‟ The maximum shear stress developed in the shaft is 60 N/mm2. A hole of 50 mm diameter is now drilled throughout the length of the shaft. To develop a maximum shear stress of 60 N/mm2 in the hollow shaft, the torque 'T‟ must be reduced by:a)T/4b)T/8c)T/12d)T/16Correct answer is option 'D'. 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 A solid shaft of diameter 100 mm, length 1000 mm is subjected to a twisting moment 'T‟ The maximum shear stress developed in the shaft is 60 N/mm2. A hole of 50 mm diameter is now drilled throughout the length of the shaft. To develop a maximum shear stress of 60 N/mm2 in the hollow shaft, the torque 'T‟ must be reduced by:a)T/4b)T/8c)T/12d)T/16Correct answer is option 'D'. Can you explain this answer?.
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