For a solid rocket motor, the burn rate r of propellant obeys Saint-Robert's law r = a * p_c^n. For stable combustion without motor overpressure explosion, the pressure exponent n must be:
Options:
(A) greater than 1
(B) less than 1
(C) equal to 1
(D) negative
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2011 Q.49)**
**1. Problem Statement & Parameters**:
- **Module**: Flight Mechanics & Space Dynamics (2 Mark, MCQ)
- **Topic**: Static Stability & Control (Static Margin & Stick-Fixed/Free Stability)
- **Organizing Institute**: IIT Madras
- **Problem Statement**:
>
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Static Stability & Control** (Static Margin & Stick-Fixed/Free Stability) 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 **C**.
**3. Comprehensive Options Analysis**:
- **(A)** *"0 ) , 0 (t w"*: ❌ **INCORRECT**.
- **(B)** *"0 ) , (2
2
t Lx
w"*: ❌ **INCORRECT**.
- **(C)** *"0 ) , 0 (2
2
tx
w"*: ✅ **CORRECT**.
- **(D)** *"0 ) , (3
3
t Lx
w
Common Data for Questions 50 and 51:
Consider an inviscid, adiabatic flow of air at free stream Mach Number, M ∞ = 2, across a compression
corner (θ = 20°) as shown. The free stream total enthalpy is h 0∞ = 810 kJ kg-1. Assume that air is calorically
perfect with γ = 1.4, R = 287 J kg-1 K-1.
The shock angle β is"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2011 (IIT Madras) master answer key with 100% precision.
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