A finite wing has aspect ratio $AR = 8$ and Oswald efficiency factor $e = 0.85$. If the wing operates at lift coefficient $C_L = 0.5$, what is the induced drag coefficient $C_{D,i}$?

(A) 0.0117

(B) 0.0234

(C) 0.0059

(D) 0.0175

Answer Key:

A

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Governing Concept & Domain Context:** * This question evaluates **Grammar & Vocabulary** under *Verbal Aptitude* in GATE AE. 2. **Stage 2: Mathematical Derivation:** * Applying Prandtl's lifting-line theory for finite wings: $C_{D,i} = \frac{C_L^2}{\pi e AR} = \frac{(0.5)^2}{\pi (0.85)(8)} = 0.0117$. Option A is correct. 3. **Stage 3: Distractor Elimination Forensics:** * The evaluated correct answer is derived using standard physical equations. * Distractor values correspond to typical unit conversion omissions or inverted formulas. 4. **Stage 4: Common Student Trap:** * *Trap:* Using $C_L$ instead of $C_L^2$ in the induced drag formula. *Reference: John D. Anderson Jr., Fundamentals of Aerodynamics (McGraw-Hill).*

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