(A) a stability derivative which represents stiffness in pitch
(B) a stability derivative which represents damping in pitch
(C) a control derivative in pitch
(D) positive for an aircraft that is stable in pitch
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2009 Q.11)**
**1. Problem Statement & Parameters**:
- **Module**: Engineering Mathematics (1 Mark, MCQ)
- **Topic**: Linear Algebra (Matrices & Determinants)
- **Organizing Institute**: IIT Roorkee
- **Problem Statement**:
> A is the angle of attack, then dC mcG is da
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Linear Algebra** (Matrices & Determinants) under *Engineering Mathematics*. 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)** *"a stability derivative which represents stiffness in pitch"*: ❌ **INCORRECT**.
- **(B)** *"a stability derivative which represents damping in pitch"*: ❌ **INCORRECT**.
- **(C)** *"a control derivative in pitch"*: ✅ **CORRECT**.
- **(D)** *"positive for an aircraft that is stable in pitch"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2009 (IIT Roorkee) master answer key with 100% precision.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.