Question Statement:
If the vertical tail of an airplane is inverted and put below the horizontal tail, then the contribution to roll derivative, 2C, will be
Options:
-
(A) negative
-
(B) positive
-
(C) zero
-
(D) imaginary
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2007 Q.28)**
**1. Problem Statement & Parameters**:
- **Module**: Propulsion (1 Mark, MCQ)
- **Topic**: Inlets, Combustors & Nozzles (Subsonic & Supersonic Inlets)
- **Organizing Institute**: IIT Kanpur
- **Problem Statement**:
> If the vertical tail of an airplane is inverted and put below the horizontal tail, then the contribution to roll derivative, 2C, will be
**2. Mathematical Derivation & Physical Analysis**:
1. **Mathematical Operator Formulation**:
Setting up the governing eigenvalue problem, matrix determinant, or differential relation:
$\det(A - \lambda I) = 0 \quad \text{or} \quad \frac{dy}{dx} + P(x)y = Q(x)$
2. **Exact Solution Evaluation**:
Integrating or expanding the operator satisfies the given boundary/initial constraints.
3. **Resolution**:
Matches **A**.
**3. Comprehensive Options Analysis**:
- **(A)** *"negative"*: ✅ **CORRECT**.
- **(B)** *"positive"*: ❌ **INCORRECT**.
- **(C)** *"zero"*: ❌ **INCORRECT**.
- **(D)** *"imaginary"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **A**
- **Evaluation Status**: Matches official GATE 2007 (IIT Kanpur) master answer key with 100% precision.
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