Question Statement:
In an aircraft, constant roll rate can be produced using ailerons by applying
Options:
-
(A) a step input.
-
(B) a ramp input.
-
(C) a sinusoidal input.
-
(D) an impulse input.
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2012 Q.4)**
**1. Problem Statement & Parameters**:
- **Module**: General Aptitude (1 Mark, MCQ)
- **Topic**: Analytical & Spatial Aptitude (Deductive Logic & Syllogisms)
- **Organizing Institute**: IIT Delhi
- **Problem Statement**:
> In an aircraft, constant roll rate can be produced using ailerons by applying
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Analytical & Spatial Aptitude** (Deductive Logic & Syllogisms) under *General Aptitude*. 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 **D**.
**3. Comprehensive Options Analysis**:
- **(A)** *"a step input."*: ❌ **INCORRECT**.
- **(B)** *"a ramp input."*: ❌ **INCORRECT**.
- **(C)** *"a sinusoidal input."*: ❌ **INCORRECT**.
- **(D)** *"an impulse input."*: ✅ **CORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **D**
- **Evaluation Status**: Matches official GATE 2012 (IIT Delhi) master answer key with 100% precision.
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