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Two shafts A and B are of same length and subjected to same torque T. If the diameter of shaft B is twice that of shaft A, the ratio of shear stresses developed in shafts A and B is
- a)8
- b)1/8
- c)1
- d)1/2
Correct answer is option 'A'. Can you explain this answer?
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Two shafts A and B are of same length and subjected to same torque T....
Given: We know,
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τ = 
= 23 = 8
Most Upvoted Answer
Two shafts A and B are of same length and subjected to same torque T....
Explanation:
To find the ratio of shear stresses developed in shafts A and B, we can use the formula for shear stress:
Shear stress (τ) = Torque (T) / Polar moment of inertia (J)
The polar moment of inertia (J) is given by:
J = π/32 * (d^4 - d_i^4)
Where,
d = diameter of the shaft
d_i = inner diameter of the shaft
Step 1: Finding the polar moment of inertia for shaft A
Let the diameter of shaft A be 'd'. Since the diameter of shaft B is twice that of shaft A, the diameter of shaft B will be '2d'.
The inner diameter of both shafts is not given, so we can assume it to be negligible. Therefore, d_i = 0.
J_A = π/32 * (d^4 - 0^4)
= π/32 * d^4
Step 2: Finding the polar moment of inertia for shaft B
J_B = π/32 * ((2d)^4 - 0^4)
= π/32 * 16d^4
= 4π/32 * d^4
= π/8 * d^4
Step 3: Finding the ratio of shear stresses
The torque applied on both shafts A and B is the same, i.e., T.
So, the ratio of shear stresses developed in shafts A and B is given by:
τ_A / τ_B = T / J_A / (T / J_B)
= J_B / J_A
= (π/8 * d^4) / (π/32 * d^4)
= (1/8)
Therefore, the ratio of shear stresses developed in shafts A and B is 1/8.
Hence, the correct answer is option A.
To find the ratio of shear stresses developed in shafts A and B, we can use the formula for shear stress:
Shear stress (τ) = Torque (T) / Polar moment of inertia (J)
The polar moment of inertia (J) is given by:
J = π/32 * (d^4 - d_i^4)
Where,
d = diameter of the shaft
d_i = inner diameter of the shaft
Step 1: Finding the polar moment of inertia for shaft A
Let the diameter of shaft A be 'd'. Since the diameter of shaft B is twice that of shaft A, the diameter of shaft B will be '2d'.
The inner diameter of both shafts is not given, so we can assume it to be negligible. Therefore, d_i = 0.
J_A = π/32 * (d^4 - 0^4)
= π/32 * d^4
Step 2: Finding the polar moment of inertia for shaft B
J_B = π/32 * ((2d)^4 - 0^4)
= π/32 * 16d^4
= 4π/32 * d^4
= π/8 * d^4
Step 3: Finding the ratio of shear stresses
The torque applied on both shafts A and B is the same, i.e., T.
So, the ratio of shear stresses developed in shafts A and B is given by:
τ_A / τ_B = T / J_A / (T / J_B)
= J_B / J_A
= (π/8 * d^4) / (π/32 * d^4)
= (1/8)
Therefore, the ratio of shear stresses developed in shafts A and B is 1/8.
Hence, the correct answer is option A.
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Two shafts A and B are of same length and subjected to same torque T. If the diameter of shaft B is twice that of shaft A, the ratio of shear stresses developed in shafts A and B isa) 8b) 1/8c) 1d) 1/2Correct answer is option 'A'. Can you explain this answer?
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Two shafts A and B are of same length and subjected to same torque T. If the diameter of shaft B is twice that of shaft A, the ratio of shear stresses developed in shafts A and B isa) 8b) 1/8c) 1d) 1/2Correct 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 Two shafts A and B are of same length and subjected to same torque T. If the diameter of shaft B is twice that of shaft A, the ratio of shear stresses developed in shafts A and B isa) 8b) 1/8c) 1d) 1/2Correct 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 Two shafts A and B are of same length and subjected to same torque T. If the diameter of shaft B is twice that of shaft A, the ratio of shear stresses developed in shafts A and B isa) 8b) 1/8c) 1d) 1/2Correct answer is option 'A'. Can you explain this answer?.
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Two shafts A and B are of same length and subjected to same torque T. If the diameter of shaft B is twice that of shaft A, the ratio of shear stresses developed in shafts A and B isa) 8b) 1/8c) 1d) 1/2Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Two shafts A and B are of same length and subjected to same torque T. If the diameter of shaft B is twice that of shaft A, the ratio of shear stresses developed in shafts A and B isa) 8b) 1/8c) 1d) 1/2Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Two shafts A and B are of same length and subjected to same torque T. If the diameter of shaft B is twice that of shaft A, the ratio of shear stresses developed in shafts A and B isa) 8b) 1/8c) 1d) 1/2Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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