List of top Questions asked in GATE Aerospace Engineering

A uniform rigid prismatic bar of total mass $ m $ is suspended from a ceiling by two identical springs as shown in the figure.
Let $ \omega_1 $ and $ \omega_2 $ be the natural frequencies of mode I and mode II respectively (with $ \omega_1<\omega_2 $).
The value of $ \omega_2/\omega_1 $ is _________ (rounded off to one decimal place).

An ideal ramjet is to operate with exhaust gases optimally expanded to ambient pressure at an altitude where temperature is 220 K. The exhaust speed at the nozzle exit is 1200 m/s at a temperature of 1100 K.
Given: $ \gamma = 1.4 $ at 220 K; $ R = 287 \, \text{J/(kg-K)} $ for air; $ \gamma = 1.33 $ at 1100 K; $ R = 287 \, \text{J/(kg-K)} $ for exhaust gases.
The cruise speed of this ramjet is _________ m/s (rounded off to nearest integer).

A multistage axial compressor takes in air at 1 atm, 300 K and compresses it to a minimum of 5 atm.
The mean blade speed is 245 m/s and work coefficient, $ \frac{\Delta c \, \theta}{U} $, is 0.55 for each stage.
For air, use $ C_p = 1005 \, \text{J/(kg-K)} $, $ R = 287 \, \text{J/(kg-K)} $, and $ \gamma = 1.4 $.
If the compression is isentropic, the number of stages required is _________ (rounded off to the next higher integer).

Consider a thin symmetric airfoil at a 2 degree angle of attack in a uniform flow at 50 m/s. The pitching moment coefficient about its leading edge is _________ (rounded off to three decimal places).

A convergent-divergent nozzle with adiabatic walls is designed for an exit Mach number of 2.3. It is discharging air to atmosphere under the conditions indicated in the figure.
Flow through the nozzle is inviscid, the characteristic gas constant for air is 287 J/(kg-K), and $ \gamma = 1.4 $.
When the reservoir pressure is 25 bar (absolute), and temperature is 300 K, Prandtl-Meyer expansion waves appear at the nozzle exit as shown.
The minimum percentage change in the reservoir pressure required to eliminate the wave system at the nozzle exit under steady state is _________ %.

A conventional airplane of mass 5000 kg is doing a level turn of radius 1000 m at a constant speed of 100 m/s at sea level.
Taking the acceleration due to gravity as 10 m/s$^2$, the bank angle of the airplane is _________ degrees.

Given: The tip deflection and tip slope for a tip-loaded cantilever of length $ L $ are: \[ \delta = \frac{NL^3}{3EI} \quad \text{and} \quad \theta = \frac{NL^2}{2EI}, \] where $ N $ is the tip force and $ EI $ is the flexural rigidity.
A cantilever $ PQ $ of rectangular cross-section is subjected to transverse load, $ F $, at its mid-point. Two cases are considered as shown in the figure. In Case I, the end $ Q $ is free and in Case II, $ Q $ is simply supported.
The ratio of the magnitude of the maximum bending stress at $ P $ in Case I to that in Case II is _________ (rounded off to one decimal place).

A simply supported Aluminium column of length 1 m and rectangular cross-section $ w \times t $ with $ t \leq w $, is subjected to axial compressive loading.
Young’s modulus is 70 GPa. Yield stress under uniaxial compression is 120 MPa.
The value of $ t $ at which the failure load for yielding and buckling coincide is _________ mm.

A 0.5 m long thin-walled circular shaft of radius 2 cm is to be designed for an axial load of 7.4 kN and a torque of 148 Nm applied at its tip, as shown in the figure.
The allowable stress under uniaxial tension is 100 MPa.
Using the maximum principal stress criterion, the minimum thickness, $ t $, of the shaft so that it does not fail is _________ mm (rounded off to the nearest integer).

A 10 kN axial load is applied eccentrically on a rod of square cross-section (1 cm $\times$ 1 cm) as shown in the figure.
The strains measured by the two strain gages attached to the top and bottom surfaces at a distance of 0.5 m from the tip are $ \varepsilon_1 = 0.0016 $ and $ \varepsilon_2 = 0.0004 $, respectively.
The eccentricity in loading, $ e $, is _________ mm.

For a thin-walled I section, the width of the two flanges as well as the web height are the same, i.e., $ 2b = 20 \, \text{mm} $. Thickness is 0.6 mm.
The second moment of area about a horizontal axis passing through the centroid is _________ mm$^4$.

Consider a high Earth-orbiting satellite of angular momentum per unit mass $\vec{h}$ and eccentricity $e$. The mass of the Earth is $M$ and $G$ is the universal gravitational constant. The distance between the satellite’s center of mass and the Earth’s center of mass is $r$, the true anomaly is $\theta$, and the phase angle is zero. Which of the following statements is/are true?

A rocket operates at an absolute chamber pressure of 20 bar to produce thrust $F_1$. The hot exhaust is optimally expanded to 1 bar (absolute pressure) using a convergent-divergent nozzle with exit to throat area ratio $\left(\frac{A_e}{A_t}\right)$ of 3.5 and thrust coefficient, $C_{F,1} = 1.42$. The same rocket when operated at an absolute chamber pressure of 50 bar produces thrust $F_2$ and the thrust coefficient is $C_{F,2}$. Which of the following statement(s) is/are correct?

The vector field $ \vec{v} = x^3 \hat{i} + y^3 \hat{j} + z^3 \hat{k} $ is a vector field where $ \hat{i}, \hat{j}, \hat{k} $ are the base vectors of a Cartesian coordinate system.
Using the Gauss divergence theorem, the value of the outward flux of the vector field over the surface of a sphere of unit radius centered at the origin is _________ (rounded off to one decimal place).

The largest eigenvalue of the given matrix is: \[ \begin{bmatrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{bmatrix} \]

A rotational velocity field in an air flow is given as $ \vec{V} = a y \hat{i} + b x \hat{j} $, with $ a = 10 \, \text{s}^{-1} $, $ b = 20 \, \text{s}^{-1} $. The air density is 1.0 kg/m$^3$ and the pressure at $ (x, y) = (0, 0) $ is 100 kPa. Neglecting gravity, the pressure at $ (x, y) = (6 \, \text{m}, 8 \, \text{m}) $ is _________ kPa (rounded off to the nearest integer).

Consider a circulation distribution over a finite wing given by the equation below.
\[ \Gamma(y) = \begin{cases} \Gamma_0 \left(1 - \frac{2y}{b}\right) & \text{if } 0 \leq y \leq \frac{b}{2}, \\ \Gamma_0 \left(1 + \frac{2y}{b}\right) & \text{if } -\frac{b}{2} \leq y \leq 0, \end{cases} \] The wingspan $ b $ is 10 m, the maximum circulation $ \Gamma_0 $ is 20 m$^2$/s, density of air is 1.2 kg/m$^3$, and the free stream speed is 80 m/s.
The lift over the wing is _________ N (rounded off to the nearest integer).

Consider a solid cylinder housed inside another cylinder as shown in the figure. Radius of the inner cylinder is 1 m and its height is 2 m. The gap between the cylinders is 5 mm and is filled with a fluid of viscosity $ 10^{-4} $ Pa-s.
The inner cylinder is rotating at a constant angular speed of 5 rad/s while the outer cylinder is stationary. Friction at the bottom surfaces can be ignored. Velocity profile in the vertical gap between the cylinders can be assumed to be linear.
The driving moment required for the rotating motion of the inner cylinder is _________ Nm (rounded off to two decimal places).

In a converging duct, area and velocity at section P are 1 m$^2$ and 15 m/s, respectively. The temperature of the fluid is 300 K.
Air flow through the nozzle can be assumed to be inviscid and isothermal. Characteristic gas constant is 287 J/(kg-K) and the ratio of specific heats is 1.4 for air.
To ensure that the air flow remains incompressible (Mach number, $ M \leq 0.3 $) in the duct, the minimum area required at section Q is _________ m$^2$ (rounded off to two decimal places).

A cylindrical object of diameter 900 mm is designed to move axially in air at 60 m/s. Its drag is estimated on a geometrically half-scaled model in water, assuming flow similarity. Co-efficients of dynamic viscosity and densities for air and water are $1.86 \times 10^{-5}$ Pa-s, 1.2 kg/m$^3$ and $1.01 \times 10^{-3}$ Pa-s, 1000 kg/m$^3$ respectively. Drag measured for the model is 2280 N. Drag experienced by the full-scale object is ___ N (rounded off to the nearest integer).

Consider a conventional subsonic fixed-wing airplane. $e$ is the Oswald efficiency factor and $AR$ is the aspect ratio. Corresponding to the minimum $\left(\frac{C_D}{C_L^{3/2}}\right)$, which of the following relations is true?

A horizontal load $F$ is applied at point R on a two-member truss, as shown in the figure. Both the members are prismatic with cross-sectional area $A_0$, and made of the same material with Young's modulus $E$. The horizontal displacement of point R is:

Which of the following is NOT always true for a combustion process taking place in a closed system?

The real function $ y = \sin^2(|x|) $ is

A convergent nozzle fed from a constant pressure, constant temperature reservoir, is discharging air to atmosphere at 1 bar (absolute) with choked flow at the exit (marked as $Q$).
Flow through the nozzle can be assumed to be isentropic.
If the exit area of the nozzle is increased while all the reservoir parameters and ambient conditions remain the same, then at steady state