Subtopic: Brayton Cycle with Real Component Efficiencies
Question Statement:
If the center of gravity of an airplane is moved forward towards the nose of the airplane; the ma. (maximum value of the lift coefficient) value for which the airplane can be trimmed (C, = 0) will
Options:
(A) decrease
(B) increase
(C) remain same
(D) depend upon
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2007 Q.26)**
**1. Problem Statement & Parameters**:
- **Module**: Propulsion (1 Mark, MCQ)
- **Topic**: Thermodynamic Cycles of Gas Turbines (Brayton Cycle with Real Component Efficiencies)
- **Organizing Institute**: IIT Kanpur
- **Problem Statement**:
> If the center of gravity of an airplane is moved forward towards the nose of the airplane; the ma. (maximum value of the lift coefficient) value for which the airplane can be trimmed (C, = 0) will
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Thermodynamic Cycles of Gas Turbines** (Brayton Cycle with Real Component Efficiencies) 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)** *"decrease"*: ❌ **INCORRECT**.
- **(B)** *"increase"*: ✅ **CORRECT**.
- **(C)** *"remain same"*: ❌ **INCORRECT**.
- **(D)** *"depend upon"*: ❌ **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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