GATE AG 2007 • Q72 MCQ • 1 Mark

Section 3: Farm Power

Tractors and Power Tillers

Subtopic: Traction theory

Question Statement:

A 35 kW two-wheel drive tractor weighing 20 kN is fitted with 6-16 8PR tyre at the front axle and 13.6-28 12PR tyre at the rear axle. The ratio of section height and section width for all tyres is 0.75. The tractor has a wheel base of 2.1 m and the center of gravity is located 0.7 m ahead of the rear axle center on a horizontal plane. The tractor is to be towed on a level ground having sandy clay loam soil at 10% moisture content with a cone index of 1200 kPa. Rolling resistance of each of the front wheels is

Options:

  • (A) 0.244 kN
  • (B) 0.354 kN
  • (C) 0.575 kN
  • (D) 0.707 kN

Official Answer Key:

A

Step-by-Step Solution & Explanation

Front tyre 6–16: b=6 in=0.1524 m, rim dia=16 in=0.4064 m, h=0.75×0.1524=0.1143 m, d=0.4064+0.2286=0.635 m. Load on each front wheel = (35% of 20 kN)/2 = 3.5 kN. Wheel numeric, C_n = CI·b·d/W = 1200×0.1524×0.635/3.5 = 33.18. Rolling-resistance coefficient (Wismer–Luth form), R_c = 1/C_n + 0.04 = 0.0301+0.04 = 0.0701. Rolling resistance per wheel = R_c×W = 0.0701×3.5 = ≈0.244 kN.

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