GATE AG 2008 • Q73 MCQ • 2 Marks

Section 6: Agricultural Process Engineering

Size Reduction and Material Handling

Subtopic: Mechanics and energy requirement in size reduction of agriculture produce

Question Statement:

A material consisting of 20 mm particles is crushed to an average size of 5 mm and requires 18 kJ kg⁻¹ energy for this size reduction. If other conditions are similar, the energy required (kJ kg⁻¹) to crush the material from 25 mm to 3 mm needs to be calculated. The energy requirement calculated using Bond's law will be

Options:

  • (A) 57.34
  • (B) 30.57
  • (C) 15.79
  • (D) 11.25

Official Answer Key:

B

Step-by-Step Solution & Explanation

Bond's law: E = K_B(1/√L₂ − 1/√L₁). Calibrate: 18 = K_B(1/√5 − 1/√20) = K_B(0.4472−0.2236) = K_B×0.2236 → K_B = 80.5. Apply to 25→3 mm: E = 80.5×(1/√3−1/√25) = 80.5×(0.5774−0.2000) = 80.5×0.3774 = 30.38 ≈ 30.57 kJ/kg.

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