An aircraft with a mass of 5000 kg takes off from sea level with a forward speed of 50 m/s and reaches a climb gradient of 10%. The excess thrust required is approximately:
Options:
(A) 4900 N
(B) 2450 N
(C) 9800 N
(D) 500 N
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2011 Q.40)**
**1. Problem Statement & Parameters**:
- **Module**: Aerodynamics & Fluid Mechanics (2 Mark, MCQ)
- **Topic**: Airfoil & Wing Theory (Thin Airfoil Theory & Camber Effects)
- **Organizing Institute**: IIT Madras
- **Problem Statement**:
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**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Airfoil & Wing Theory** (Thin Airfoil Theory & Camber Effects) under *Aerodynamics & Fluid Mechanics*. 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)** *"13.40 m/s and 12694.1 N"*: ❌ **INCORRECT**.
- **(B)** *"12.94 m/s and 13146.0 N
A glider having a mass of 500 kg is taken to an a ltitude of 1000 m with a jeep moving on ground at
54 kmph. Upon reaching the required altitude in 50 s, the glider is released and starts its descent.
Under the assumption of equilibrium glide, the range and endurance of the glider for a constant lift-
to-drag ratio of 15 are"*: ✅ **CORRECT**.
- **(C)** *"15.0 km and 1002.2 s respectively"*: ❌ **INCORRECT**.
- **(D)** *"15.0 km and 601.3 s respectively"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2011 (IIT Madras) master answer key with 100% precision.