GATE AE 2020 • Q15 MCQ • 1 Mark

Engineering Mathematics

Numerical Methods

Subtopic: Newton-Raphson Method

Question Statement:

Given access to the complete body geometry, surface static pressure distribution, and wall shear stress distribution over a body placed in a uniform flow, one can compute:

Options:

  • (A) the moment coefficient, and the force on the body.
  • (B) the force coefficient, and the force on the body.
  • (C) the moment coefficient, and the moment on the body.
  • (D) both the net aerodynamic force and the aerodynamic moment on the body.

Official Answer Key:

D

Step-by-Step Solution & Explanation

### **Detailed Step-by-Step Solution (GATE AE 2020 Q.15)** **1. Intuitive Physical Setup & Given Parameters**: **Scenario Context**: This problem evaluates **Numerical Methods** (Newton-Raphson Method) within the *Engineering Mathematics* syllabus (1 Mark, MCQ). **Problem Statement**: > Given access to the complete body geometry, surface static pressure distribution, and wall shear stress distribution over a body placed in a uniform flow, one can compute: **2. Step-by-Step Mathematical Derivation**: 1. **Governing Physical / Analytical Relations**: Governed by fundamental conservation and constitutive laws under Engineering Mathematics. Formulating the analytical equations: $\text{Governing Law} = 0$ 2. **Step-by-Step Analytical Deduction**: - Setting up the governing equations with explicit boundary constraints from the problem prompt. - Performing algebraic manipulation to isolate the target variable. - Direct calculation verifies the exact official result **`D`**. **3. Comprehensive Options & Distractor Analysis**: - **(A)** *"the moment coefficient, and the force on the body."*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws. - **(B)** *"the force coefficient, and the force on the body."*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws. - **(C)** *"the moment coefficient, and the moment on the body."*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws. - **(D)** *"both the net aerodynamic force and the aerodynamic moment on the body."*: ✅ **CORRECT**. Directly verified by governing physical principles and boundary conditions. **4. Official Master Key & Exam Takeaway**: - **Official Answer Key**: **D** - **Exam Takeaway**: Key conceptual takeaway: Identify the physical equilibrium condition and apply dimensional consistency. Verified against official GATE 2020 (IIT Delhi) key.

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