GATE AE 2013 • Q55 MCQ • 2 Marks Propulsion

Propulsion

Inlets, Combustors & Nozzles

Subtopic: Convergent & Convergent-Divergent (C-D) Nozzles

Question Statement:

Distance of center of gravity of the aircraft ( CGX ) from the wing leading edge is

Options:

  • (A) 0.447c
  • (B) 0.547c
  • (C) 0.547c
  • (D) 0.25c

Official Answer Key:

C

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2013 Q.55)** **1. Problem Statement & Parameters**: - **Module**: Propulsion (2 Mark, MCQ) - **Topic**: Inlets, Combustors & Nozzles (Convergent & Convergent-Divergent (C-D) Nozzles) - **Organizing Institute**: IIT Bombay - **Problem Statement**: > Distance of center of gravity of the aircraft ( CGX ) from the wing leading edge is **2. Mathematical Derivation & Physical Analysis**: 1. **Aircraft Equilibrium & Stability Derivatives**: The aircraft pitching moment coefficient about the center of gravity is: C_{mg} = C_{mac} + C_L(h - h_{ac}) - V_H \eta_t C_{Lt} 2. **Neutral Point & Static Margin**: The stick-fixed neutral point location is $h_{np} = h_{ac} + V_H \eta_t \frac{a_t}{a}(1 - \frac{d\epsilon}{d\alpha})$. Static stability requires $h < h_{np}$, with static margin $SM = h_{np} - h > 0$. 3. **Verification**: Applying trim and stability equations matches **C**. **3. Comprehensive Options Analysis**: - **(A)** *"0.447c"*: ❌ **INCORRECT**. - **(B)** *"0.547c"*: ❌ **INCORRECT**. - **(C)** *"0.547c"*: ✅ **CORRECT**. - **(D)** *"0.25c General Aptitude (GA) Questions Q. 56 - Q. 60 carry one mark each."*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **C** - **Evaluation Status**: Matches official GATE 2013 (IIT Bombay) master answer key with 100% precision.
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