Subtopic: Functional requirements, principles of working, construction and operation of manual, animal, tractor and renewable energy operated equipment for tillage, sowing, planting, fertilizer application, inter-cultivation, spraying, mowing, chaff cutting, harvesting and threshing
Question Statement:
A bushy crop with stem cross-sectional diameter 6 mm is to be cut by impact force at a height of 50 mm above the soil surface. Based on the entire stem cross-section, the modulus of elasticity is 1500 N·mm⁻² and ultimate tensile strength is 35 N·mm⁻². The force in N that would cause failure of the stem due to bending is (Take π = 3.14)
Options:
(A) 14.84
(B) 23.52
(C) 29.69
(D) 44.53
Official Answer Key:
A
Step-by-Step Solution & Explanation
Moment of inertia of circular stem: I = πd⁴/64 = 3.14×6⁴/64 = 3.14×1296/64 = 63.6 mm⁴. Failure bending moment: M = σ_ult × I / c, where c = d/2 = 3 mm: M = 35×63.6/3 = 742.1 N·mm. Force at height L=50 mm: F = M/L = 742.1/50 = 14.84 N, matching (A).
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