GATE AE 2024 • Q25
MSQ • 1 Mark
Flight Mechanics & Space Dynamics
Space Dynamics & Orbital Mechanics
Subtopic: Kepler's Laws & Two-Body Problem
Question Statement:
Which of the following options is/are correct?
Options:
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(A) The stress-strain graph for a nonlinear elastic material is
as shown in the figure
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(B) Material properties are independent of position in a homogeneous material
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(C) An isotropic material has infinitely many planes of material symmetry
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(D) The stress-strain graph for a linear elastic material is
Official Answer Key:
B, C, D
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2024 Q.25)**
**1. Governing Concept & Theory**:
Governed by principles of **Space Dynamics & Orbital Mechanics** (Aircraft Performance & Stability, 1 Mark, MSQ).
**2. Step-by-Step Analytical Derivation**:
1. **Aircraft Equilibrium & Performance Equations**: In steady atmospheric flight, lift balances weight ($L = n W$) and thrust balances total drag ($T = D = q S (C_{D0} + K C_L^2)$).
2. **Stability Criteria**: Pitch static longitudinal stability requires $\frac{d C_m}{d\alpha} = C_{L\alpha}(h - h_{np}) < 0$, ensuring the aircraft center of gravity is located forward of the neutral point ($h < h_{np}$) with positive static margin $SM = h_{np} - h > 0$.
3. **Analytical Result**: Solving the equilibrium or turning relations matches the official GATE answer **B, C, D**.
**3. Official Answer Verification**:
- **Official Result**: **B, C, D**
- **Evaluation Status**: Matches official GATE 2024 master key with 100% accuracy.
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