The critical Mach number of an airfoil is attained when
Options:
(A) the freestream Mach number is sonic.
(B) the freestream Mach number is supersonic.
(C) the Mach number somewhere on the airfoil is unity.
(D) the Mach number everywhere on the airfoil is supersonic.
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2012 Q.6)**
**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 **(C)** (`the Mach number somewhere on the airfoil is unity.`) 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 **(C)** is the unique correct answer.
**3. Official Answer Verification**:
- **Official Result**: **C**
- **Evaluation Status**: Matches official GATE 2012 master key with 100% accuracy.
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