GATE AG 2019 • Q42 MCQ • 2 Marks

Section 3: Farm Power

Tractors and Power Tillers

Subtopic: Mechanics of tractor chassis

Question Statement:

Tractors and Power tillers: Type, selection, maintenance and repair of tractors and power tillers; tractor clutches and brakes; power transmission systems – gear trains, differential, final drives and power take-off; mechanics of tractor chassis; traction theory; three point hitches - free link and restrained link operations; steering and hydraulic control systems used in tractors; tractor tests and performance; human engineering and safety considerations in design of tractor and agricultural implements. A two-wheel drive tractor operating a plough at forward speed 5 km/h experiences wheel slip of 15%. If the angular speed of the rear axle is 2.4 rad/s, the rolling radius of the traction wheel in metres will be

Options:

  • (A) 0.49
  • (B) 0.58
  • (C) 0.68
  • (D) 0.75

Official Answer Key:

C

Step-by-Step Solution & Explanation

Slip, s = (theoretical speed − actual speed)/theoretical speed, so actual (forward) speed = theoretical speed × (1 − s). Actual speed = 5 km/h = 5/3.6 = 1.389 m/s. Theoretical speed = ω × r, so actual speed = ω·r·(1−s) → r = actual speed / [ω(1−s)] r = 1.389 / [2.4 × (1 − 0.15)] = 1.389 / (2.4 × 0.85) = 1.389/2.04 = 0.681 ≈ 0.68 m. Answer: (C) 0.68.

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