Subtopic: Overload safety devices used in farm machinery
Question Statement:
The standard of a cultivator experiences a maximum bending moment of 120 Nm. It has a rectangular cross-section with sides in the ratio of 3:1. If the permissible bending stress of the material is 8 × 10⁷ N m⁻², the cross-sectional area of the cultivator standard in square millimeter is
Options:
(A) 222
(B) 300
(C) 492
(D) 624
Official Answer Key:
B
Step-by-Step Solution & Explanation
Bending equation: M = σ·Z, section modulus for a rectangle Z = b·d²/6. With d = 3b (ratio 3:1), Z = b(3b)²/6 = 1.5b³. σ = M/Z ⟹ Z = M/σ = 120/(8×10⁷) = 1.5×10⁻⁶ m³. b³ = Z/1.5 = 1×10⁻⁶ ⟹ b = 0.01 m = 10 mm; d = 3b = 30 mm. Cross-sectional area = b×d = 10×30 = 300 mm², matching option (B).
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