Relative to the forward stagnation point, the angular positions along the circumference where the speed along the surface of the cylinder is equal to the free stream speed are
Options:
(A) 30, 150, 210 and 330 degrees
(B) 45, 135, 225 and 315 degrees
(C) 0, 90, 180 and 270 degrees
(D) 60, 120, 240 and 300 degrees
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2007 Q.47)**
**1. Problem Statement & Parameters**:
- **Module**: Flight Mechanics & Space Dynamics (2 Mark, MCQ)
- **Topic**: Atmospheric Flight Mechanics (Drag Polar & Aircraft Performance Equations)
- **Organizing Institute**: IIT Kanpur
- **Problem Statement**:
> Relative to the forward stagnation point, the angular positions along the circumference where the speed along the surface of the cylinder is equal to the free stream speed are
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Atmospheric Flight Mechanics** (Drag Polar & Aircraft Performance Equations) 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 **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"30, 150, 210 and 330 degrees"*: ❌ **INCORRECT**.
- **(B)** *"45, 135, 225 and 315 degrees"*: ✅ **CORRECT**.
- **(C)** *"0, 90, 180 and 270 degrees"*: ❌ **INCORRECT**.
- **(D)** *"60, 120, 240 and 300 degrees"*: ❌ **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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