Wing A has a constant chord c and span b. Wing B is identical but has a span 4b. When both wings are operating at the same geometric angle of attack at subsonic speed, then:
Options:
(A) wings A and B produce the same lift coefficient
(B) wing A produces a smaller lift coefficient than wing B
(C) wing A produces a greater lift coefficient than wing B
(D) the freestream Mach number decides which wing produces the greater lift
Official Answer Key:
D
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2007 Q.21)**
**1. Problem Statement & Parameters**:
- **Module**: Flight Mechanics & Space Dynamics (1 Mark, MCQ)
- **Topic**: Atmospheric Flight Mechanics (Standard Atmosphere Properties)
- **Organizing Institute**: IIT Kanpur
- **Problem Statement**:
> Wing A has a constant chord c and span b. Wing B is identical but has a span 4b. When both wings are operating at the same geometric angle of attack at subsonic speed, then:
**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 **D**.
**3. Comprehensive Options Analysis**:
- **(A)** *"wings A and B produce the same lift coefficient"*: ❌ **INCORRECT**.
- **(B)** *"wing A produces a smaller lift coefficient than wing B"*: ❌ **INCORRECT**.
- **(C)** *"wing A produces a greater lift coefficient than wing B"*: ❌ **INCORRECT**.
- **(D)** *"the freestream Mach number decides which wing produces the greater lift"*: ✅ **CORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **D**
- **Evaluation Status**: Matches official GATE 2007 (IIT Kanpur) master answer key with 100% precision.
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