GATE AG 2025 • Q34 NAT • 1 Mark

Section 6: Agricultural Process Engineering

Size Reduction and Material Handling

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

Question Statement:

Find the critical speed (rpm) of a ball mill, mill diameter 3600 mm, ball diameter 160 mm (g = 9.81 m/s², π = 3.14). (Answer in integer)

Official Answer Key:

22 to 24

Step-by-Step Solution & Explanation

Critical speed Nc = (1/2π)√[g/(R−r)] (rev/s), where R = mill radius = 1.8 m, r = ball radius = 0.08 m. Nc = (1/(2×3.14))×√(9.81/1.72) rev/s = 0.15924×2.389 = 0.3803 rev/s = 22.82 rpm ≈ 23 rpm.

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