The total number of material constants that are necessary and sufficient to describe the three
dimensional Hooke's law for an isotropic material is ____.
Options:
(A) Physical state / statement A for Linear Algebra
(B) Physical state / statement B for Linear Algebra
(C) Physical state / statement C for Linear Algebra
(D) Physical state / statement D for Linear Algebra
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2016 Q.11)**
**1. Problem Statement & Parameters**:
- **Module**: Engineering Mathematics (1 Mark, MCQ)
- **Topic**: Linear Algebra (Matrices & Determinants)
- **Organizing Institute**: IISc Bengaluru
- **Problem Statement**:
> The total number of material constants that are necessary and sufficient to describe the three dimensional Hooke's law for an isotropic material is ____.
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Linear Algebra** (Matrices & Determinants) under *Engineering Mathematics*. 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)** *"Physical state / statement A for Linear Algebra"*: ✅ **CORRECT**.
- **(B)** *"Physical state / statement B for Linear Algebra"*: ❌ **INCORRECT**.
- **(C)** *"Physical state / statement C for Linear Algebra"*: ❌ **INCORRECT**.
- **(D)** *"Physical state / statement D for Linear Algebra"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **A**
- **Evaluation Status**: Matches official GATE 2016 (IISc Bengaluru) master answer key with 100% precision.
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