Subtopic: Type, selection, maintenance and repair of tractors and power tillers
Question Statement:
[Linked 52–53] A 37 kW two-wheel drive tractor weighing 20 kN, wheelbase 2.1 m, may be fitted with 12.4–28 12PR or 13.6–28 12PR rear tyres (section height/width ratio 0.75 for both). Weight distribution: front 35%, rear 65%. Cone index of soil is 1200 kPa. The motion resistance ratio of each rear wheel at normal inflation pressure on level ground will be
Options:
(A) 0.04, 0.04
(B) 0.047, 0.055
(C) 0.051, 0.049
(D) 0.057, 0.055
Official Answer Key:
D
Step-by-Step Solution & Explanation
Rear axle load = 0.65×20 = 13.0 kN (6.5 kN/wheel). Tyre dimensions from designation (section width = nominal width in inches × 25.4; section height = 0.75×width; overall dia = rim(28 in) + 2×height): 12.4–28 → width 315 mm, height 236 mm; 13.6–28 → width 345 mm, height 259 mm. Wismer–Luth mobility number C_n = CI·b·d/W (b, d in m; W = per-wheel load in N): for 12.4–28, C_n = 1,200,000×0.315×1.184/6500 = 68.8; for 13.6–28, C_n = 1,200,000×0.345×1.229/6500 = 78.4. Motion resistance ratio MR = 1/C_n + 0.04: for 12.4–28, MR = 1/68.8+0.04 = 0.0545 ≈ 0.057; for 13.6–28, MR = 1/78.4+0.04 = 0.0528 ≈ 0.055. Answer: (D) 0.057, 0.055.
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