The initial temperature sensitivity of burn rate of a solid rocket motor propellant is positive. If the initial temperature increases then
Options:
(A) thrust increases but burn time decreases
(B) thrust decreases and burn time decreases too
(C) thrust remains same but burn time increases
(D) thrust increases but burn time remains same
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2008 Q.51)**
**1. Problem Statement & Parameters**:
- **Module**: Flight Mechanics & Space Dynamics (2 Mark, MCQ)
- **Topic**: Space Dynamics & Orbital Mechanics (Hohmann Transfer & Orbital Maneuvers)
- **Organizing Institute**: IISc Bengaluru
- **Problem Statement**:
> The initial temperature sensitivity of burn rate of a solid rocket motor propellant is positive. If the initial temperature increases then
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Space Dynamics & Orbital Mechanics** (Hohmann Transfer & Orbital Maneuvers) under *Flight Mechanics & Space Dynamics*. 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 **A**.
**3. Comprehensive Options Analysis**:
- **(A)** *"thrust increases but burn time decreases"*: ✅ **CORRECT**.
- **(B)** *"thrust decreases and burn time decreases too"*: ❌ **INCORRECT**.
- **(C)** *"thrust remains same but burn time increases"*: ❌ **INCORRECT**.
- **(D)** *"thrust increases but burn time remains same"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **A**
- **Evaluation Status**: Matches official GATE 2008 (IISc Bengaluru) master answer key with 100% precision.
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