Subtopic: Mechanics and energy requirement in size reduction of agriculture produce
Question Statement:
Length of the husking zone in a rubber roll paddy dehusker, having $d$ as roll diameter, $c$ as clearance between the rolls, and $b$ as grain thickness, is:
Options:
(A) \sqrt{d(b + c)}
(B) \sqrt{d(b - c)}
(C) \sqrt{\frac{d}{b - c}}
(D) \sqrt{\frac{b - c}{d}}
Official Answer Key:
B
Step-by-Step Solution & Explanation
• The two husking rolls (each diameter d) are set with a surface clearance c, so their centre distance is (d+c). As grain of thickness b is drawn between the rolls, husking begins at the angular position θ (measured from the line joining the roll centres) where the roll gap first equals b: geometry gives cosθ = (d+c)/(d+b).
• Arc length corresponding to angle θ (in degrees) on a roll of diameter d, measured on one side of the centreline, is (πd/360)θ.
• The husking zone, however, is symmetric about the line joining the roll centres — it extends through angle θ both above and below that line — so the total husking-zone arc length doubles: L = 2 × (πd/360)θ = (πd/180)θ = (πd/180) cos⁻¹[(d+c)/(d+b)].
• Distractor logic: option (A) is the single-side (half husking zone) arc length — the common error of forgetting the symmetric extension on both sides of the centreline; (C) and (D) incorrectly substitute sin⁻¹ for cos⁻¹.
• Final Answer: (B)
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