Subtopic: Stress and Strain Tensors & Generalized Hooke's Law
Question Statement:
If the vessel is evacuated (internal pressure = 0) and subjected to external pressure, yielding
according to the von Mises yield criterion (assuming elastic stability until yield)
Options:
(A) occurs at about half the pressure Yp .
(B) occurs at about double the pressure Yp .
(C) occurs at about the same pressure Yp .
(D) never occurs.
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2012 Q.55)**
**1. Problem Statement & Parameters**:
- **Module**: Propulsion (2 Mark, MCQ)
- **Topic**: Inlets, Combustors & Nozzles (Convergent & Convergent-Divergent (C-D) Nozzles)
- **Organizing Institute**: IIT Delhi
- **Problem Statement**:
> If the vessel is evacuated (internal pressure = 0) and subjected to external pressure, yielding according to the von Mises yield criterion (assuming elastic stability until yield)
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Inlets, Combustors & Nozzles** (Convergent & Convergent-Divergent (C-D) Nozzles) under *Propulsion*. 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)** *"occurs at about half the pressure Yp ."*: ❌ **INCORRECT**.
- **(B)** *"occurs at about double the pressure Yp ."*: ❌ **INCORRECT**.
- **(C)** *"occurs at about the same pressure Yp ."*: ✅ **CORRECT**.
- **(D)** *"never occurs.
2012 GENERAL APTITUDE - GA_AN_Online
General Aptitude (GA) Questions
Q. 56 - Q. 60 carry one mark each.
Choose the most appropriate alternative from the options given below to complete the following
sentence:
I ___ to have bought a diamond ring."*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2012 (IIT Delhi) master answer key with 100% precision.