GATE 2024 AE question paper PDF and answer key

Joining the 54 cm edges makes a tube of length 54 cm and circumference 4 cm: $r = 2/\pi$, $V = \pi r^2 \times 54 = 216/\pi$. The cube has $6a^2 = 216$, so $a = 6$ and $V = 216$. Ratio $= 1/\pi$.

The rudder provides yaw control: coordinating turns (A), countering asymmetric thrust (B) and crosswind landings (C). It plays no role in longitudinal (pitch) stability.

Point Q is the corner of the V-n diagram where the stall ($C_{L,max}$) curve meets the limit load factor: the corner speed, giving the maximum turn rate and minimum turn radius. Drag there is high, not minimum.

The shaded portion is the cap above the chord at height $R\cos 60° = R/2$; rotating it about the y-axis gives a spherical cap of height $h = R/2$:

$V = \frac{\pi h^2(3R - h)}{3} = \frac{\pi (R^2/4)(5R/2)}{3} = \frac{5}{24}\pi R^3.$

BC is a two-force member at 45°. Taking moments about the pin A for bar ACD: the 100 N load at D (1.0 m below A, 30° from vertical) has horizontal component 50 N, giving 50 N·m. BC acts at C (0.5 m below A) with horizontal component $F\cos 45°$: $F\cos 45° \times 0.5 = 50$, so $F = 141.4$ N.