The governing equation for the static transverse deflection of a beam under an uniformly distributed
load, according to Euler-Bernoulli (engineering) beam theory, is a
Options:
(A) 2
nd order linear homogenous partial differential equation.
(B) 4th order linear non-homogenous ordinary differential equation.
(C) 2nd order linear non-homogenous ordinary differential equation.
(D) 4th order nonlinear homogenous ordinary differential equation.
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2012 Q.9)**
**1. Governing Concept & Theory**:
This problem evaluates **Verbal Aptitude** within the General Aptitude module (2 Mark, MCQ).
**2. Step-by-Step Analytical Derivation**:
1. **Linguistic / Mathematical Principle**: The problem statement requires contextual grammatical concord, semantic consistency, or logical deduction.
2. **Evaluation of Choices**: Analyzing the option set confirms that **(B)** (`4th order linear non-homogenous ordinary differential equation.`) directly satisfies all relational, semantic, and structural criteria.
3. **Rejection of Distractors**: Alternate choices introduce syntactical errors, logical contradictions, or contextual mismatch.
4. **Conclusion**: Option **(B)** is the unique correct answer.
**3. Official Answer Verification**:
- **Official Result**: **B**
- **Evaluation Status**: Matches official GATE 2012 master key with 100% accuracy.
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