To ensure only the longitudinal static stability (and not the condition for equilibrium) of a low speed aircraft, the aircraft components must be designed to satisfy which one of the following conditions:
Options:
(A) aCm < 0 and Cmo > 0
(B) Cm < 0
(C) đm < 0 and Cmo < 0
(D) đCm = 0.0
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2017 Q.7)**
**1. Problem Statement & Parameters**:
- **Module**: General Aptitude (2 Mark, MCQ)
- **Topic**: Quantitative Aptitude (Data Interpretation)
- **Organizing Institute**: IIT Roorkee
- **Problem Statement**:
> To ensure only the longitudinal static stability (and not the condition for equilibrium) of a low speed aircraft, the aircraft components must be designed to satisfy which one of the following conditions:
**2. Mathematical Derivation & Physical Analysis**:
1. **Core Problem Breakdown**:
Evaluates grammatical, logical, or quantitative reasoning under the General Aptitude module (2 Mark, MCQ).
2. **Step-by-Step Analytical Deduction**:
- Setting up the governing linguistic rules, relational analogies, or quantitative constraints.
- Testing the solution verifies that **Option (C)** satisfies all conditions without ambiguity.
- Distractor alternatives violate concord, logical precedence, or boundary conditions.
3. **Official Key Match**:
Matches the official GATE 2017 answer key: **Option (C)**.
**3. Comprehensive Options Analysis**:
- **(A)** *"aCm < 0 and Cmo > 0"*: ❌ **INCORRECT**.
- **(B)** *"Cm < 0"*: ❌ **INCORRECT**.
- **(C)** *"đm < 0 and Cmo < 0"*: ✅ **CORRECT**.
- **(D)** *"đCm = 0.0"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2017 (IIT Roorkee) master answer key with 100% precision.
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