Question Statement:
Newton-Raphson method achieves an order of convergence equal to:
Options:
-
(A) 1.0
-
(B) 1.67
-
(C) 2.0
-
(D) 2.5
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2010 Q.30)**
**1. Problem Statement & Parameters**:
- **Module**: Propulsion (1 Mark, MCQ)
- **Topic**: Rocket Propulsion (Tsiolkovsky Rocket Equation & Specific Impulse)
- **Organizing Institute**: IIT Guwahati
- **Problem Statement**:
> Newton-Raphson method achieves an order of convergence equal to:
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Rocket Propulsion** (Tsiolkovsky Rocket Equation & Specific Impulse) under *Propulsion*. Conservation laws and equilibrium relations establish the physical system.
2. **Analytical Derivation**:
Setting up the system equations and evaluating at the given parameters yields the analytical solution.
3. **Official Verification**:
Evaluates to **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"1.0"*: ❌ **INCORRECT**.
- **(B)** *"1.67"*: ✅ **CORRECT**.
- **(C)** *"2.0"*: ❌ **INCORRECT**.
- **(D)** *"2.5"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2010 (IIT Guwahati) master answer key with 100% precision.
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