A wire of 0.1 mm dia is drawn from a rod of 15 mm diameter

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A wire of 0.1 mm dia is drawn from a rod of 15 mm diameter dies giving reductions of 20%, 40% and 80% are available. For minimum error in the final size, the number of stages and reduction at each stage respectively would be

1. 3 stages and 80% reduction for all three stages
2. 4 stages and 80% reduction for first three stages followed by a finishing stage of 20% reduction
3. 5 stage and reduction of 80%, 80%, 40%, 40%, 20% is sequence
4. None of these

Correct Option: B

% reduction =	Diameter reduced in draw
	Diameter before draw

for option (a) =	d₀ - d₁	= 0.8
	d₀

d₁ = 2d₀
Given d₀ = 15 mm , we get d₁ = 3 mm
Similarly, after 2nd pass, we get d₂ = 0.6 mm and after 3rd pass, we get d₃ = 0.12 mm For option (b), 1st 3 stages are same as in option (a), in 4th pass we have

	d₃ - d₄	= 0.2
	d₃

⇒ d₄ = 0.8d₃
⇒ d₄ = 0.8 × 0.12 = 0.096 mm
For option (c), first two stages are same as in option (a), in 3rd pass we have

	d₃ - d₄	= 0.4
	d₃

⇒ d₃ = 6 , d₂ = 0.6 × 0.6 = 0.36 mm
For 4th pass we have

	d₃ - d₄	= 0.4
	d₃

⇒ d₄ = 0.6 , d₃ = 0.6 × 0.36 = 0.216 mm
For 5th stage, we have

	d₅ - d₄	= 0.2
	d₄

⇒ d₅ = 0.8 , d₄ = 0.8 × 0.216 = 0.1728 mm
Output in option (b) is closest to the desired diameter of 0.1 mm