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Two solid cylinders of equal diameter have different heights. They are compressed plastically by a pair of rigid dies to create the same percentage reduction in their respective heights. Consider that the die-workpiece interface friction is negligible. The ratio of the final diameter of the shorter cylinder to that of the longer cylinder is __________
(Important - Enter only the numerical value in the answer)
Correct answer is '1'. Can you explain this answer?
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Two solid cylinders of equal diameter have different heights. They are...
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Two solid cylinders of equal diameter have different heights. They are...
Explanation:
To solve this problem, let's consider the initial and final dimensions of the two cylinders.
Let:
- D = diameter of the cylinders
- h1 = initial height of the shorter cylinder
- h2 = initial height of the longer cylinder
- h1' = final height of the shorter cylinder
- h2' = final height of the longer cylinder
Since both cylinders are compressed plastically by the same percentage reduction in their heights, we can set up the following equation:
(h1 - h1') / h1 = (h2 - h2') / h2
Step 1: Finding the final height of the longer cylinder
Since both cylinders have the same initial diameter, the percentage reduction in height is the same for both. Therefore, we can write:
(h1 - h1') / h1 = (h2 - h2') / h2
Simplifying this equation, we get:
h1' / h1 = h2' / h2
Cross-multiplying, we get:
h1' * h2 = h1 * h2'
Step 2: Finding the ratio of the final diameters
The initial and final volumes of the cylinders are the same since the material is incompressible. Therefore, we can write:
π * (D/2)^2 * h1 = π * (D/2)^2 * h1'
Cancelling out the common terms, we get:
h1 = h1'
Similarly, we can write:
π * (D/2)^2 * h2 = π * (D/2 * r)^2 * h2'
Cancelling out the common terms and simplifying, we get:
(D/2)^2 * h2 = (D/2 * r)^2 * h2'
D^2 * h2 = (D * r)^2 * h2'
Dividing both sides by h2 and taking the square root, we get:
D = D * r
Simplifying, we get:
1 = r
Therefore, the ratio of the final diameter of the shorter cylinder to that of the longer cylinder is 1.
To solve this problem, let's consider the initial and final dimensions of the two cylinders.
Let:
- D = diameter of the cylinders
- h1 = initial height of the shorter cylinder
- h2 = initial height of the longer cylinder
- h1' = final height of the shorter cylinder
- h2' = final height of the longer cylinder
Since both cylinders are compressed plastically by the same percentage reduction in their heights, we can set up the following equation:
(h1 - h1') / h1 = (h2 - h2') / h2
Step 1: Finding the final height of the longer cylinder
Since both cylinders have the same initial diameter, the percentage reduction in height is the same for both. Therefore, we can write:
(h1 - h1') / h1 = (h2 - h2') / h2
Simplifying this equation, we get:
h1' / h1 = h2' / h2
Cross-multiplying, we get:
h1' * h2 = h1 * h2'
Step 2: Finding the ratio of the final diameters
The initial and final volumes of the cylinders are the same since the material is incompressible. Therefore, we can write:
π * (D/2)^2 * h1 = π * (D/2)^2 * h1'
Cancelling out the common terms, we get:
h1 = h1'
Similarly, we can write:
π * (D/2)^2 * h2 = π * (D/2 * r)^2 * h2'
Cancelling out the common terms and simplifying, we get:
(D/2)^2 * h2 = (D/2 * r)^2 * h2'
D^2 * h2 = (D * r)^2 * h2'
Dividing both sides by h2 and taking the square root, we get:
D = D * r
Simplifying, we get:
1 = r
Therefore, the ratio of the final diameter of the shorter cylinder to that of the longer cylinder is 1.
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Two solid cylinders of equal diameter have different heights. They are compressed plastically bya pair of rigid dies to create the same percentage reduction in their respective heights. Considerthat the die-workpiece interface friction is negligible. The ratio of the final diameter of theshorter cylinder to that of the longer cylinder is __________(Important - Enter only the numerical value in the answer)Correct answer is '1'. Can you explain this answer?
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Two solid cylinders of equal diameter have different heights. They are compressed plastically bya pair of rigid dies to create the same percentage reduction in their respective heights. Considerthat the die-workpiece interface friction is negligible. The ratio of the final diameter of theshorter cylinder to that of the longer cylinder is __________(Important - Enter only the numerical value in the answer)Correct answer is '1'. 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 Two solid cylinders of equal diameter have different heights. They are compressed plastically bya pair of rigid dies to create the same percentage reduction in their respective heights. Considerthat the die-workpiece interface friction is negligible. The ratio of the final diameter of theshorter cylinder to that of the longer cylinder is __________(Important - Enter only the numerical value in the answer)Correct answer is '1'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two solid cylinders of equal diameter have different heights. They are compressed plastically bya pair of rigid dies to create the same percentage reduction in their respective heights. Considerthat the die-workpiece interface friction is negligible. The ratio of the final diameter of theshorter cylinder to that of the longer cylinder is __________(Important - Enter only the numerical value in the answer)Correct answer is '1'. Can you explain this answer?.
Two solid cylinders of equal diameter have different heights. They are compressed plastically bya pair of rigid dies to create the same percentage reduction in their respective heights. Considerthat the die-workpiece interface friction is negligible. The ratio of the final diameter of theshorter cylinder to that of the longer cylinder is __________(Important - Enter only the numerical value in the answer)Correct answer is '1'. 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 Two solid cylinders of equal diameter have different heights. They are compressed plastically bya pair of rigid dies to create the same percentage reduction in their respective heights. Considerthat the die-workpiece interface friction is negligible. The ratio of the final diameter of theshorter cylinder to that of the longer cylinder is __________(Important - Enter only the numerical value in the answer)Correct answer is '1'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two solid cylinders of equal diameter have different heights. They are compressed plastically bya pair of rigid dies to create the same percentage reduction in their respective heights. Considerthat the die-workpiece interface friction is negligible. The ratio of the final diameter of theshorter cylinder to that of the longer cylinder is __________(Important - Enter only the numerical value in the answer)Correct answer is '1'. Can you explain this answer?.
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