GATE AE 2012 • Q32 MCQ • 1 Mark Aerospace Structures

Aerospace Structures

Strength of Materials & Elasticity

Subtopic: Airframe Structural Analysis & Trusses

Question Statement:

The volume of a solid generated by rotating the region between semi-circle 211y x=- - and straight line y = 1, about x axis, is

Options:

  • (A) 2 4 3$\pi \pi$-
  • (B) 2 14 3$\pi \pi$-
  • (C) 2 3 4 $\pi \pi$-
  • (D) 23 4 $\pi \pi$-

Official Answer Key:

A

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2012 Q.32)** **1. Problem Statement & Parameters**: - **Module**: Aerospace Structures (1 Mark, MCQ) - **Topic**: Strength of Materials & Elasticity (Airframe Structural Analysis & Trusses) - **Organizing Institute**: IIT Delhi - **Problem Statement**: > The volume of a solid generated by rotating the region between semi-circle 211y x=- - and straight line y = 1, about x axis, is **2. Mathematical Derivation & Physical Analysis**: 1. **Governing Physical Principles**: Governed by **Strength of Materials & Elasticity** (Airframe Structural Analysis & Trusses) 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 **A**. **3. Comprehensive Options Analysis**: - **(A)** *"2 4 3$\pi \pi$-"*: ✅ **CORRECT**. - **(B)** *"2 14 3$\pi \pi$-"*: ❌ **INCORRECT**. - **(C)** *"2 3 4 $\pi \pi$-"*: ❌ **INCORRECT**. - **(D)** *"23 4 $\pi \pi$-"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **A** - **Evaluation Status**: Matches official GATE 2012 (IIT Delhi) master answer key with 100% precision.
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