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GATE 2020 ME (ME1) – Question 42

Casting, Forming and Joining Processes · Bulk forming and sheet forming, estimation of load · 2 marks · Multiple choice

A 40 mm thick strip is rolled to 20 mm in a two-high mill with rolls of diameter 200 mm. Estimate the coefficient of friction and arc length (mm), respectively.

  1. 0.45 and 38.84
  2. 0.39 and 38.84
  3. 0.39 and 44.72
  4. 0.45 and 44.72

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Correct answer: (D) 0.45 and 44.72

Explanation

Using the usual small-angle rolling estimates, maximum draft Δh=μ²R and contact length $l=\sqrt{R\Delta h}$. With R=100 mm, Δh=20 mm, μ=√0.2=0.447≈0.45 and l=√2000=44.72 mm. **Answer: D.** These are approximate rolling relations, not the exact circular arc length.