GATE Exam > GATE Questions > A solid shaft of diameter 40 mm is used in po...
Start Learning for Free
A solid shaft of diameter 40 mm is used in power transmission. Due to modification of existing transmission system, it is required to replace the solid shaft by a hollow shaft of same material & equally strong in torsion. Find the outer diameter of hollow shaft (in mm)_______, if ratio of inner diameter to outer diameter is 0.6.
Correct answer is between '41.5,42.3'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A solid shaft of diameter 40 mm is used in power transmission. Due to ...
And same length. The outside diameter of the hollow shaft is 60 mm and the inside diameter is 30 mm. Determine the ratio of torsional rigidity of the hollow shaft to the solid shaft.
To determine the ratio of torsional rigidity, we need to calculate the polar moment of inertia for both the solid and hollow shafts.
For the solid shaft:
The diameter of the solid shaft is 40 mm, so the radius (r) is 20 mm = 0.02 m.
The polar moment of inertia (J) for a solid shaft is given by the formula:
J = (π/32) * (d^4)
where d is the diameter of the shaft.
J_solid = (π/32) * (0.04^4) = 0.00002513 m^4
For the hollow shaft:
The outside diameter of the hollow shaft is 60 mm, so the outer radius (r1) is 30 mm = 0.03 m.
The inside diameter of the hollow shaft is 30 mm, so the inner radius (r2) is 15 mm = 0.015 m.
The polar moment of inertia (J) for a hollow shaft is given by the formula:
J = (π/32) * (d1^4 - d2^4)
where d1 is the outside diameter and d2 is the inside diameter of the shaft.
J_hollow = (π/32) * ((0.06^4) - (0.03^4)) = 0.00016965 m^4
The ratio of torsional rigidity (G) for the hollow shaft to the solid shaft is given by the formula:
G_hollow/solid = J_hollow/J_solid
G_hollow/solid = 0.00016965 m^4 / 0.00002513 m^4
G_hollow/solid = 6.76
Therefore, the ratio of torsional rigidity of the hollow shaft to the solid shaft is 6.76.
To determine the ratio of torsional rigidity, we need to calculate the polar moment of inertia for both the solid and hollow shafts.
For the solid shaft:
The diameter of the solid shaft is 40 mm, so the radius (r) is 20 mm = 0.02 m.
The polar moment of inertia (J) for a solid shaft is given by the formula:
J = (π/32) * (d^4)
where d is the diameter of the shaft.
J_solid = (π/32) * (0.04^4) = 0.00002513 m^4
For the hollow shaft:
The outside diameter of the hollow shaft is 60 mm, so the outer radius (r1) is 30 mm = 0.03 m.
The inside diameter of the hollow shaft is 30 mm, so the inner radius (r2) is 15 mm = 0.015 m.
The polar moment of inertia (J) for a hollow shaft is given by the formula:
J = (π/32) * (d1^4 - d2^4)
where d1 is the outside diameter and d2 is the inside diameter of the shaft.
J_hollow = (π/32) * ((0.06^4) - (0.03^4)) = 0.00016965 m^4
The ratio of torsional rigidity (G) for the hollow shaft to the solid shaft is given by the formula:
G_hollow/solid = J_hollow/J_solid
G_hollow/solid = 0.00016965 m^4 / 0.00002513 m^4
G_hollow/solid = 6.76
Therefore, the ratio of torsional rigidity of the hollow shaft to the solid shaft is 6.76.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
A solid shaft of diameter 40 mm is used in power transmission. Due to modification of existing transmission system, it is required to replace the solid shaft by a hollow shaft of same material & equally strong in torsion. Find the outer diameter of hollow shaft (in mm)_______, if ratio of inner diameter to outer diameter is 0.6.Correct answer is between '41.5,42.3'. Can you explain this answer?
Question Description
A solid shaft of diameter 40 mm is used in power transmission. Due to modification of existing transmission system, it is required to replace the solid shaft by a hollow shaft of same material & equally strong in torsion. Find the outer diameter of hollow shaft (in mm)_______, if ratio of inner diameter to outer diameter is 0.6.Correct answer is between '41.5,42.3'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A solid shaft of diameter 40 mm is used in power transmission. Due to modification of existing transmission system, it is required to replace the solid shaft by a hollow shaft of same material & equally strong in torsion. Find the outer diameter of hollow shaft (in mm)_______, if ratio of inner diameter to outer diameter is 0.6.Correct answer is between '41.5,42.3'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid shaft of diameter 40 mm is used in power transmission. Due to modification of existing transmission system, it is required to replace the solid shaft by a hollow shaft of same material & equally strong in torsion. Find the outer diameter of hollow shaft (in mm)_______, if ratio of inner diameter to outer diameter is 0.6.Correct answer is between '41.5,42.3'. Can you explain this answer?.
A solid shaft of diameter 40 mm is used in power transmission. Due to modification of existing transmission system, it is required to replace the solid shaft by a hollow shaft of same material & equally strong in torsion. Find the outer diameter of hollow shaft (in mm)_______, if ratio of inner diameter to outer diameter is 0.6.Correct answer is between '41.5,42.3'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A solid shaft of diameter 40 mm is used in power transmission. Due to modification of existing transmission system, it is required to replace the solid shaft by a hollow shaft of same material & equally strong in torsion. Find the outer diameter of hollow shaft (in mm)_______, if ratio of inner diameter to outer diameter is 0.6.Correct answer is between '41.5,42.3'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid shaft of diameter 40 mm is used in power transmission. Due to modification of existing transmission system, it is required to replace the solid shaft by a hollow shaft of same material & equally strong in torsion. Find the outer diameter of hollow shaft (in mm)_______, if ratio of inner diameter to outer diameter is 0.6.Correct answer is between '41.5,42.3'. Can you explain this answer?.
Solutions for A solid shaft of diameter 40 mm is used in power transmission. Due to modification of existing transmission system, it is required to replace the solid shaft by a hollow shaft of same material & equally strong in torsion. Find the outer diameter of hollow shaft (in mm)_______, if ratio of inner diameter to outer diameter is 0.6.Correct answer is between '41.5,42.3'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of A solid shaft of diameter 40 mm is used in power transmission. Due to modification of existing transmission system, it is required to replace the solid shaft by a hollow shaft of same material & equally strong in torsion. Find the outer diameter of hollow shaft (in mm)_______, if ratio of inner diameter to outer diameter is 0.6.Correct answer is between '41.5,42.3'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A solid shaft of diameter 40 mm is used in power transmission. Due to modification of existing transmission system, it is required to replace the solid shaft by a hollow shaft of same material & equally strong in torsion. Find the outer diameter of hollow shaft (in mm)_______, if ratio of inner diameter to outer diameter is 0.6.Correct answer is between '41.5,42.3'. Can you explain this answer?, a detailed solution for A solid shaft of diameter 40 mm is used in power transmission. Due to modification of existing transmission system, it is required to replace the solid shaft by a hollow shaft of same material & equally strong in torsion. Find the outer diameter of hollow shaft (in mm)_______, if ratio of inner diameter to outer diameter is 0.6.Correct answer is between '41.5,42.3'. Can you explain this answer? has been provided alongside types of A solid shaft of diameter 40 mm is used in power transmission. Due to modification of existing transmission system, it is required to replace the solid shaft by a hollow shaft of same material & equally strong in torsion. Find the outer diameter of hollow shaft (in mm)_______, if ratio of inner diameter to outer diameter is 0.6.Correct answer is between '41.5,42.3'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A solid shaft of diameter 40 mm is used in power transmission. Due to modification of existing transmission system, it is required to replace the solid shaft by a hollow shaft of same material & equally strong in torsion. Find the outer diameter of hollow shaft (in mm)_______, if ratio of inner diameter to outer diameter is 0.6.Correct answer is between '41.5,42.3'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
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