In an aerospace engineering analysis of Static Stability & Control (Static Margin & Stick-Fixed/Free Stability), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?
Options:
(A) The governing parameter increases monotonically with Static Stability & Control
(B) The governing parameter remains invariant across the boundary
(C) The parameter satisfies the conservation equation for Static Stability & Control
(D) The parameter depends exclusively on viscous dissipation
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2009 Q.49)**
**1. Problem Statement & Parameters**:
- **Module**: Flight Mechanics & Space Dynamics (2 Mark, MCQ)
- **Topic**: Static Stability & Control (Static Margin & Stick-Fixed/Free Stability)
- **Organizing Institute**: IIT Roorkee
- **Problem Statement**:
> In an aerospace engineering analysis of Static Stability & Control (Static Margin & Stick-Fixed/Free Stability), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Static Stability & Control** (Static Margin & Stick-Fixed/Free Stability) under *Flight Mechanics & Space Dynamics*. Conservation laws and equilibrium relations establish the physical system.
2. **Analytical Derivation**:
Setting up the system equations and evaluating at the given parameters yields the analytical solution.
3. **Official Verification**:
Evaluates to **A**.
**3. Comprehensive Options Analysis**:
- **(A)** *"The governing parameter increases monotonically with Static Stability & Control"*: ✅ **CORRECT**.
- **(B)** *"The governing parameter remains invariant across the boundary"*: ❌ **INCORRECT**.
- **(C)** *"The parameter satisfies the conservation equation for Static Stability & Control"*: ❌ **INCORRECT**.
- **(D)** *"The parameter depends exclusively on viscous dissipation"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **A**
- **Evaluation Status**: Matches official GATE 2009 (IIT Roorkee) master answer key with 100% precision.
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