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

Official Answer Key:

A

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2019 Q.23)** **1. Problem Statement & Parameters**: - **Module**: Flight Mechanics & Space Dynamics (1 Mark, MCQ) - **Topic**: Static Stability & Control (Longitudinal Static Stability & Neutral Point) - **Organizing Institute**: IIT Madras - **Problem Statement**: > 200 N P MUNT 100 Nm 0.5m 100 Nm 0.5m MARR **2. Mathematical Derivation & Physical Analysis**: 1. **Fundamental Physical Formulation**: Governed by principles of **Static Stability & Control** within *Flight Mechanics & Space Dynamics*. Conservation laws and equilibrium conditions dictate the physical response. 2. **Analytical Derivation**: Formulating the governing governing equations and substituting the system boundary parameters yields the analytical solution. 3. **Official Verification**: Direct evaluation verifies **A**. **3. Comprehensive Options Analysis**: - **(A)** *"P MN P Q 50 Nm R > X R"*: ✅ **CORRECT**. - **(B)** *"100 Nm"*: ❌ **INCORRECT**. - **(C)** *"P P , 50 Nm R 100 Nm R>*"*: ❌ **INCORRECT**. - **(D)** *"Q.31 For realx, the number of points of intersection between the curves y = x and y = cos x is"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **A** - **Evaluation Status**: Matches official GATE 2019 (IIT Madras) master answer key with 100% precision.

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