GATE AE 2007 • Q62 MCQ • 2 Marks Aerospace Structures

Aerospace Structures

Thin-Walled Structures

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

Question Statement:

The natural frequencies c of the fixed-free rod can then be obtained using

Options:

  • (A) cos("') = 0
  • (B) sin(°) = 0
  • (C) cos(°°) = 0
  • (D) cos(=) =0

Official Answer Key:

D

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2007 Q.62)** **1. Problem Statement & Parameters**: - **Module**: Aerospace Structures (2 Mark, MCQ) - **Topic**: Thin-Walled Structures (Tension Field Beams & Wagner Beams) - **Organizing Institute**: IIT Kanpur - **Problem Statement**: > The natural frequencies c of the fixed-free rod can then be obtained using **2. Mathematical Derivation & Physical Analysis**: 1. **Governing Physical Principles**: Governed by **Thin-Walled Structures** (Tension Field Beams & Wagner Beams) 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 **D**. **3. Comprehensive Options Analysis**: - **(A)** *"cos("') = 0"*: ❌ **INCORRECT**. - **(B)** *"sin(°) = 0"*: ❌ **INCORRECT**. - **(C)** *"cos(°°) = 0"*: ❌ **INCORRECT**. - **(D)** *"cos(=) =0"*: ✅ **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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