GATE AE 2008 • Q50
MCQ • 2 Marks
Flight Mechanics & Space Dynamics
Dynamic Stability
Subtopic: Dutch Roll, Spiral & Roll Subsidence Modes
Question Statement:
MJ/kg, the fuel to air ratio is
Options:
-
(A) 0.003
-
(B) 0.012
-
(C) 0.031
-
(D) 0.074
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2008 Q.50)**
**1. Problem Statement & Parameters**:
- **Module**: Flight Mechanics & Space Dynamics (2 Mark, MCQ)
- **Topic**: Dynamic Stability (Dutch Roll, Spiral & Roll Subsidence Modes)
- **Organizing Institute**: IISc Bengaluru
- **Problem Statement**:
> MJ/kg, the fuel to air ratio is
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Dynamic Stability** (Dutch Roll, Spiral & Roll Subsidence Modes) 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)** *"0.003"*: ✅ **CORRECT**.
- **(B)** *"0.012"*: ❌ **INCORRECT**.
- **(C)** *"0.031"*: ❌ **INCORRECT**.
- **(D)** *"0.074"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **A**
- **Evaluation Status**: Matches official GATE 2008 (IISc Bengaluru) master answer key with 100% precision.
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