GATE AE 2023 • Q47
MSQ • 2 Marks
Flight Mechanics & Space Dynamics
Atmospheric Flight Mechanics
Subtopic: Drag Polar & Aircraft Performance Equations
Question Statement:
Which of the following statement(s) about the elastic flexural buckling load of
columns is/are correct?
Options:
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(A) The buckling load increases with increase in flexural rigidity of the column.
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(B) The buckling load increases with increase in the length of the column.
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(C) The boundary conditions of the column affect the buckling load.
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(D) The buckling load is NOT directly dependent on the density of the material used
for the column.
Official Answer Key:
A, C, D
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2023 Q.47)**
**1. Governing Concept & Theory**:
Governed by principles of **Atmospheric Flight Mechanics** (Aircraft Performance & Stability, 2 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 **A, C, D**.
**3. Official Answer Verification**:
- **Official Result**: **A, C, D**
- **Evaluation Status**: Matches official GATE 2023 master key with 100% accuracy.
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