GATE AG 2025 • Q58 NAT • 2 Marks

Section 2: Farm Machinery

Farm Machinery

Subtopic: Hitch systems and hitching of tillage implements

Question Statement:

A mouldboard plough is operated by a 2WD tractor; the resultant soil-reaction pull is 6.0 kN. Lateral:longitudinal force ratio = 0.30, vertical:longitudinal ratio = 0.50. Driving-wheel diameter = 1.2 m, rear axle speed = 10 rpm, wheel slip = 20%. Find drawbar power (kW). (Rounded to 2 decimal places)

Official Answer Key:

2.30 to 2.90

Step-by-Step Solution & Explanation

With longitudinal component = F_l, lateral = 0.30F_l, vertical = 0.50F_l, the resultant magnitude = F_l√(1+0.30²+0.50²) = 1.1576 F_l. Given resultant pull = 6.0 kN ⇒ F_l (draft) = 6.0/1.1576 = 5.183 kN. Theoretical peripheral speed = ωr = (10×2π/60)×0.6 = 0.6283 m/s. Actual travel speed = theoretical×(1−slip) = 0.6283×0.80 = 0.5027 m/s. Drawbar power = F_l × v_actual = 5.183×0.5027 = 2.61 kW.

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