GATE ME 2021 Set 2 — Question 51
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Manufacturing Processes → Forming → Plastic Deformation & Yield Criteria
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Question
The thickness, width and length of a metal slab are 50 mm, 250 mm and 3600 mm, respectively. A rolling operation on this slab reduces the thickness by 10% and increases the width by 3%. The length of the rolled slab is __________ mm (round off to one decimal place).
Correct answer
3880 to 3886
Solution
Let the initial thickness, width, and length be , , and respectively. Let the final thickness, width, and length be , , and respectively.Given:
mm
mm
mmThe rolling operation reduces the thickness by 10%. So, the final thickness is:
mmThe rolling operation increases the width by 3%. So, the final width is:
mmIn a rolling process, the volume of the material remains constant. This is the principle of volume constancy.
Initial Volume () = Final Volume ()
We need to find the final length, .
Substituting the given values:
mmThe question asks to round off the answer to one decimal place.
mm.The official answer key provides a range from 3880.0 to 3886.0, and our calculated value falls within this range.
mm
mm
mmThe rolling operation reduces the thickness by 10%. So, the final thickness is:
mmThe rolling operation increases the width by 3%. So, the final width is:
mmIn a rolling process, the volume of the material remains constant. This is the principle of volume constancy.
Initial Volume () = Final Volume ()
We need to find the final length, .
Substituting the given values:
mmThe question asks to round off the answer to one decimal place.
mm.The official answer key provides a range from 3880.0 to 3886.0, and our calculated value falls within this range.
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