GATE AE 2014 • Q50
MCQ • 2 Marks
Flight Mechanics & Space Dynamics
Dynamic Stability
Subtopic: Dutch Roll, Spiral & Roll Subsidence Modes
Question Statement:
A cryogenic rocket has a specific impulse of 455s and characteristic velocity of 2386 m/s. The
value of thrust coefficient for this rocket is
Options:
-
(A) 1.78
-
(B) 1.73
-
(C) 1.87
-
(D) 1.95
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2014 Q.50)**
**1. Governing Concept & Theory**:
Governed by principles of **Dynamic Stability** (Aircraft Performance & Stability, 2 Mark, MCQ).
**2. Step-by-Step Analytical Derivation**:
1. **Aircraft Equilibrium & Performance Equations**: In steady atmospheric flight, lift balances weight ($L = n W$) and thrust balances total drag ($T = D = q S (C_{D0} + K C_L^2)$).
2. **Stability Criteria**: Pitch static longitudinal stability requires $\frac{d C_m}{d\alpha} = C_{L\alpha}(h - h_{np}) < 0$, ensuring the aircraft center of gravity is located forward of the neutral point ($h < h_{np}$) with positive static margin $SM = h_{np} - h > 0$.
3. **Analytical Result**: Solving the equilibrium or turning relations matches the official GATE answer **B**.
**3. Official Answer Verification**:
- **Official Result**: **B**
- **Evaluation Status**: Matches official GATE 2014 master key with 100% accuracy.
- **Selected Option**: **(B)** — *"1.73"*
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.
Launch CBT Mock Test