GATE AE 2011 • Q50
MCQ • 2 Marks
Flight Mechanics & Space Dynamics
Dynamic Stability
Subtopic: Dutch Roll, Spiral & Roll Subsidence Modes
Question Statement:
The specific impulse I_sp of a rocket engine is defined as:
Options:
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(A) Thrust / (propellant mass flow rate * g_0)
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(B) Thrust * propellant mass flow rate
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(C) Total impulse / burn time
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(D) Chamber pressure / throat area
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2011 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**: IIT Madras
- **Problem Statement**:
>
**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 **D**.
**3. Comprehensive Options Analysis**:
- **(A)** *"= 20°"*: ❌ **INCORRECT**.
- **(B)** *"> 20° and< 30°"*: ❌ **INCORRECT**.
- **(C)** *"= 30° "*: ❌ **INCORRECT**.
- **(D)** *"> 30°
The total temperature at point P is Q.51"*: ✅ **CORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **D**
- **Evaluation Status**: Matches official GATE 2011 (IIT Madras) master answer key with 100% precision.
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