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A strip of thickness 40 mm is to be rolled to a thickness of 20 mm using a two-high mill having rolls of diameter 200 mm. Coefficient of friction and arc length in mm, respectively are
  • a)
    0.45 and 44.72
  • b)
    0.45 and 38.84
  • c)
    0.39 and 38.84
  • d)
    0.39 and 44.72
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A strip of thickness 40 mm is to be rolled to a thickness of 20 mm usi...
h0 = 40 mm, hf = 20 mm, Δh = 40 – 20 = 20 mm, D = 200 mm, R = 100 mm Projected length,
L = 
Δh = μ2R
∴ 20 = μ2⋅100
∴ 0.2 = μ2
μ = 0.4472
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Most Upvoted Answer
A strip of thickness 40 mm is to be rolled to a thickness of 20 mm usi...
To determine the coefficient of friction and arc length in a rolling process, we can use the following formulas:
Friction force (F) = (π/2) * (μ * W * R)
Arc length (L) = (π/2) * (d1 + d2)
Where:
μ is the coefficient of friction
W is the width of the strip
R is the roll radius
d1 is the initial thickness of the strip
d2 is the final thickness of the strip

Given:
Initial thickness (d1) = 40 mm
Final thickness (d2) = 20 mm
Roll diameter (D) = 200 mm

Let's calculate the coefficient of friction (μ) first:

1. Calculate the roll radius (R):
R = D/2 = 200/2 = 100 mm

2. Calculate the width of the strip (W):
W = 2 * R = 2 * 100 = 200 mm

3. Calculate the friction force (F):
F = (π/2) * (μ * W * R)

4. Rearrange the formula to solve for μ:
μ = F / ((π/2) * W * R)

Next, let's calculate the arc length (L):

5. Calculate the initial and final diameter of the strip:
Initial diameter (d1) = 2 * R + 2 * d1 = 2 * 100 + 2 * 40 = 280 mm
Final diameter (d2) = 2 * R + 2 * d2 = 2 * 100 + 2 * 20 = 240 mm

6. Calculate the arc length (L):
L = (π/2) * (d1 + d2)

Now, let's substitute the given values into the formulas and calculate the results:

1. Calculate the coefficient of friction (μ):
μ = F / ((π/2) * W * R)

2. Calculate the arc length (L):
L = (π/2) * (d1 + d2)

Based on the calculations, the correct answer is option 'A':
- The coefficient of friction (μ) is 0.45
- The arc length (L) is 44.72 mm.
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A strip of thickness 40 mm is to be rolled to a thickness of 20 mm using a two-high mill having rolls of diameter 200 mm. Coefficient of friction and arc length in mm, respectively area)0.45 and 44.72b)0.45 and 38.84c)0.39 and 38.84d)0.39 and 44.72Correct answer is option 'A'. Can you explain this answer?
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