Question Statement:
The most aft location of the airplane center of gravity permitted to fulfill designer's requirement on longitudinal static stability is
Options:
-
(A) 0.35 c
-
(B) 0.45 c
-
(C) 0.52 c
-
(D) 0.67 c
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2007 Q.54)**
**1. Problem Statement & Parameters**:
- **Module**: Propulsion (2 Mark, MCQ)
- **Topic**: Thermodynamic Cycles of Gas Turbines (Thrust Equations & Specific Fuel Consumption)
- **Organizing Institute**: IIT Kanpur
- **Problem Statement**:
> The most aft location of the airplane center of gravity permitted to fulfill designer's requirement on longitudinal static stability is
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Thermodynamic Cycles of Gas Turbines** (Thrust Equations & Specific Fuel Consumption) under *Propulsion*. 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 **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"0.35 c"*: ❌ **INCORRECT**.
- **(B)** *"0.45 c"*: ✅ **CORRECT**.
- **(C)** *"0.52 c"*: ❌ **INCORRECT**.
- **(D)** *"0.67 c"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2007 (IIT Kanpur) master answer key with 100% precision.
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