GATE AE 2019 • Q23
MCQ • 1 Mark
Flight Mechanics & Space Dynamics
Static Stability & Control
Subtopic: Longitudinal Static Stability & Neutral Point
Question Statement:
200 N P MUNT 100 Nm 0.5m 100 Nm 0.5m MARR
Options:
-
(A) P
MN
P
Q
50 Nm
R
> X
R
-
(B) 100 Nm
-
(C) P
P
, 50 Nm
R
100 Nm
R>*
-
(D) Q.31 For realx, the number of points of intersection between the curves y = x and y = cos x is
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2019 Q.23)**
**1. Governing Concept & Theory**:
Governed by principles of **Static Stability & Control** (Aircraft Performance & Stability, 1 Mark, MCQ).
**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**.
**3. Official Answer Verification**:
- **Official Result**: **A**
- **Evaluation Status**: Matches official GATE 2019 master key with 100% accuracy.
- **Selected Option**: **(A)** — *"P
MN
P
Q
50 Nm
R
> X
R"*
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.
Launch CBT Mock Test