Mechanical Engineering Exam > Mechanical Engineering Questions > Two shafts A and B are of same length and su...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Two shafts A and B are of same length and subjected to same torque T....
Given: We know,
View all questions of this test
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.
Attention Mechanical Engineering Students!
To make sure you are not studying endlessly, EduRev has designed Mechanical Engineering study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Mechanical Engineering.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
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?
Question Description
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?.
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?.
Solutions 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? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning 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? defined & explained in the simplest way possible. Besides giving the explanation 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?, 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
ample number of questions to practice 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? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup