If an aircraft takes off with 10% less fuel in comparison to its standard configuration, its range is
Options:
(A) lower by exactly 10%.
(B) lower by more than 10%.
(C) lower by less than 10%.
(D) an unpredictable quantity.
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2012 Q.34)**
**1. Problem Statement & Parameters**:
- **Module**: Aerospace Structures (1 Mark, MCQ)
- **Topic**: Structural Dynamics & Aeroelasticity (Flutter Phenomenon & Divergence Speed)
- **Organizing Institute**: IIT Delhi
- **Problem Statement**:
> If an aircraft takes off with 10% less fuel in comparison to its standard configuration, its range is
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Structural Dynamics & Aeroelasticity** (Flutter Phenomenon & Divergence Speed) under *Aerospace Structures*. 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)** *"lower by exactly 10%."*: ❌ **INCORRECT**.
- **(B)** *"lower by more than 10%."*: ❌ **INCORRECT**.
- **(C)** *"lower by less than 10%."*: ✅ **CORRECT**.
- **(D)** *"an unpredictable quantity."*: ❌ **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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