GATE Exam > GATE Questions > A cylindrical job with diameter of 200 mm and...
Start Learning for Free
A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulus method of riser design. Assume that the bottom surface of cylindrical riser does not contribute as cooling surface. If the diameter of the riser is equal to its height, then the height of the riser (in mm) is
- a)150
- b)200
- c)100
- d)125
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A cylindrical job with diameter of 200 mm and height of 100 mm is to b...
Most Upvoted Answer
A cylindrical job with diameter of 200 mm and height of 100 mm is to b...
To determine the height of the riser using the modulus method of riser design, we need to consider the cooling surfaces involved and the dimensions of the cylindrical job and riser.
Given:
Diameter of the cylindrical job = 200 mm
Height of the cylindrical job = 100 mm
1. Cooling Surfaces:
The bottom surface of the cylindrical riser does not contribute as a cooling surface. Therefore, only the lateral surface of the riser will be considered as a cooling surface.
2. Dimensions of the Riser:
Let's assume the diameter and height of the riser as 'D' and 'H', respectively.
3. Calculation of the Modulus:
The modulus method of riser design states that the modulus of the riser should be equal to the modulus of the job. The modulus of a cylindrical job is given by the formula:
Modulus of job = (π/4) * (D^2 - d^2) * H
Where:
D = Diameter of the job
d = Diameter of the riser
H = Height of the job
Since the diameter of the riser is equal to its height (D = H), we can rewrite the formula as:
Modulus of job = (π/4) * (D^2 - d^2) * D
4. Substituting the Given Values:
Substituting the given values into the equation, we have:
(π/4) * (200^2 - d^2) * 100 = (π/4) * (200^2 - d^2) * d
Cancelling out the common terms, the equation simplifies to:
200^2 - d^2 = d
Simplifying further:
d^2 + d - 200^2 = 0
Using the quadratic formula, we can solve for 'd':
d = (-1 ± √(1^2 - 4*1*(-200^2))) / 2*1
Simplifying further:
d = (-1 ± √(1 + 4*200^2)) / 2
d ≈ 199.5 mm (Taking the positive value)
Therefore, the approximate diameter of the riser is 199.5 mm.
Since the height of the riser is equal to its diameter (H = D), the height of the riser is approximately 199.5 mm.
However, none of the given options match this result. Therefore, it seems there may be an error in the options provided.
Given:
Diameter of the cylindrical job = 200 mm
Height of the cylindrical job = 100 mm
1. Cooling Surfaces:
The bottom surface of the cylindrical riser does not contribute as a cooling surface. Therefore, only the lateral surface of the riser will be considered as a cooling surface.
2. Dimensions of the Riser:
Let's assume the diameter and height of the riser as 'D' and 'H', respectively.
3. Calculation of the Modulus:
The modulus method of riser design states that the modulus of the riser should be equal to the modulus of the job. The modulus of a cylindrical job is given by the formula:
Modulus of job = (π/4) * (D^2 - d^2) * H
Where:
D = Diameter of the job
d = Diameter of the riser
H = Height of the job
Since the diameter of the riser is equal to its height (D = H), we can rewrite the formula as:
Modulus of job = (π/4) * (D^2 - d^2) * D
4. Substituting the Given Values:
Substituting the given values into the equation, we have:
(π/4) * (200^2 - d^2) * 100 = (π/4) * (200^2 - d^2) * d
Cancelling out the common terms, the equation simplifies to:
200^2 - d^2 = d
Simplifying further:
d^2 + d - 200^2 = 0
Using the quadratic formula, we can solve for 'd':
d = (-1 ± √(1^2 - 4*1*(-200^2))) / 2*1
Simplifying further:
d = (-1 ± √(1 + 4*200^2)) / 2
d ≈ 199.5 mm (Taking the positive value)
Therefore, the approximate diameter of the riser is 199.5 mm.
Since the height of the riser is equal to its diameter (H = D), the height of the riser is approximately 199.5 mm.
However, none of the given options match this result. Therefore, it seems there may be an error in the options provided.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulusmethod of riser design. Assume that the bottom surface of cylindrical riser does not contribute ascooling surface. If the diameter of the riser is equal to its height, then the height of the riser (inmm) isa)150b)200c)100d)125Correct answer is option 'A'. Can you explain this answer?
Question Description
A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulusmethod of riser design. Assume that the bottom surface of cylindrical riser does not contribute ascooling surface. If the diameter of the riser is equal to its height, then the height of the riser (inmm) isa)150b)200c)100d)125Correct answer is option 'A'. 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 cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulusmethod of riser design. Assume that the bottom surface of cylindrical riser does not contribute ascooling surface. If the diameter of the riser is equal to its height, then the height of the riser (inmm) isa)150b)200c)100d)125Correct answer is option 'A'. 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 cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulusmethod of riser design. Assume that the bottom surface of cylindrical riser does not contribute ascooling surface. If the diameter of the riser is equal to its height, then the height of the riser (inmm) isa)150b)200c)100d)125Correct answer is option 'A'. Can you explain this answer?.
A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulusmethod of riser design. Assume that the bottom surface of cylindrical riser does not contribute ascooling surface. If the diameter of the riser is equal to its height, then the height of the riser (inmm) isa)150b)200c)100d)125Correct answer is option 'A'. 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 cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulusmethod of riser design. Assume that the bottom surface of cylindrical riser does not contribute ascooling surface. If the diameter of the riser is equal to its height, then the height of the riser (inmm) isa)150b)200c)100d)125Correct answer is option 'A'. 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 cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulusmethod of riser design. Assume that the bottom surface of cylindrical riser does not contribute ascooling surface. If the diameter of the riser is equal to its height, then the height of the riser (inmm) isa)150b)200c)100d)125Correct answer is option 'A'. Can you explain this answer?.
Solutions for A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulusmethod of riser design. Assume that the bottom surface of cylindrical riser does not contribute ascooling surface. If the diameter of the riser is equal to its height, then the height of the riser (inmm) isa)150b)200c)100d)125Correct answer is option 'A'. 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 cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulusmethod of riser design. Assume that the bottom surface of cylindrical riser does not contribute ascooling surface. If the diameter of the riser is equal to its height, then the height of the riser (inmm) isa)150b)200c)100d)125Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulusmethod of riser design. Assume that the bottom surface of cylindrical riser does not contribute ascooling surface. If the diameter of the riser is equal to its height, then the height of the riser (inmm) isa)150b)200c)100d)125Correct answer is option 'A'. Can you explain this answer?, a detailed solution for A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulusmethod of riser design. Assume that the bottom surface of cylindrical riser does not contribute ascooling surface. If the diameter of the riser is equal to its height, then the height of the riser (inmm) isa)150b)200c)100d)125Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulusmethod of riser design. Assume that the bottom surface of cylindrical riser does not contribute ascooling surface. If the diameter of the riser is equal to its height, then the height of the riser (inmm) isa)150b)200c)100d)125Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulusmethod of riser design. Assume that the bottom surface of cylindrical riser does not contribute ascooling surface. If the diameter of the riser is equal to its height, then the height of the riser (inmm) isa)150b)200c)100d)125Correct answer is option 'A'. 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