A four-wheel-drive tractor has a static weight of 50 kN with 40% weight on rear axle and 60% on front axle. The wheel base is 2 m. The tractor is pulling a disc harrow that exerts a level drawbar pull at a hitch height of 0.5 m from the ground. During the operation, when the dynamic reaction on each axle is same, the dynamic traction ratio developed by the tractor is
Options:
(A) 0.2
(B) 0.4
(C) 0.5
(D) 0.8
Official Answer Key:
B
Step-by-Step Solution & Explanation
Static reactions: front = 0.60×50 = 30 kN, rear = 0.40×50 = 20 kN.
A level drawbar pull P at hitch height h transfers weight from front to rear axle: ΔW = P·h/L = P×0.5/2 = 0.25P.
Dynamic front reaction = 30 − 0.25P; dynamic rear reaction = 20 + 0.25P.
Setting them equal (given condition): 30 − 0.25P = 20 + 0.25P ⇒ 10 = 0.5P ⇒ P = 20 kN (check: rear = 20+5 = 25 kN = front = 30−5 = 25 kN ✓).
Dynamic traction ratio = P / (total weight) = 20/50 = 0.4. Answer: (B).
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