GATE AE 2012 • Q21
MCQ • 1 Mark
Flight Mechanics & Space Dynamics
Atmospheric Flight Mechanics
Subtopic: Standard Atmosphere Properties
Question Statement:
The ratio of flight speed to the exhaust velocity for maximum propulsion efficiency is
Options:
-
(A) 0.0
-
(B) 0.5
-
(C) 1.0
-
(D) 2.0
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2012 Q.21)**
**1. Problem Statement & Parameters**:
- **Module**: Flight Mechanics & Space Dynamics (1 Mark, MCQ)
- **Topic**: Atmospheric Flight Mechanics (Standard Atmosphere Properties)
- **Organizing Institute**: IIT Delhi
- **Problem Statement**:
> The ratio of flight speed to the exhaust velocity for maximum propulsion efficiency is
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Atmospheric Flight Mechanics** (Standard Atmosphere Properties) 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 **C**.
**3. Comprehensive Options Analysis**:
- **(A)** *"0.0"*: ❌ **INCORRECT**.
- **(B)** *"0.5"*: ❌ **INCORRECT**.
- **(C)** *"1.0"*: ✅ **CORRECT**.
- **(D)** *"2.0"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2012 (IIT Delhi) master answer key with 100% precision.
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