In general, for any given solid subjected to arbitrary loading, which of the following statements is
always true:
Options:
(A) Volume does not vary with loading
(B) Mass does not vary with loading
(C) Density does not vary with loading
(D) Volume, mass and density vary with loading
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2014 Q.12)**
**1. Problem Statement & Parameters**:
- **Module**: Engineering Mathematics (1 Mark, MCQ)
- **Topic**: Linear Algebra (Eigenvalues & Eigenvectors)
- **Organizing Institute**: IIT Kharagpur
- **Problem Statement**:
> In general, for any given solid subjected to arbitrary loading, which of the following statements is always true:
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Linear Algebra** (Eigenvalues & Eigenvectors) 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 **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"Volume does not vary with loading"*: ❌ **INCORRECT**.
- **(B)** *"Mass does not vary with loading"*: ✅ **CORRECT**.
- **(C)** *"Density does not vary with loading"*: ❌ **INCORRECT**.
- **(D)** *"Volume, mass and density vary with loading"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2014 (IIT Kharagpur) master answer key with 100% precision.
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