List of top Questions asked in GATE Aerospace Engineering

A 1 m long rod is to be designed to support an axial tensile load \( P \) (\( P >> \) weight of the rod). The material for the rod is to be chosen from one of the four provided in the table. Using strength-based failure criterion for design, which material results in the lowest weight of the rod? % Given Properties Properties:
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\( \delta Q \) and \( \delta W \) are the heat and work interactions of a system with its surroundings, and \( dU \) is the change in the internal energy of the system. For an adiabatic process in a closed, constant pressure combustor, which one of the following options is correct?
The lift per unit span for a spinning circular cylinder in a potential flow is 6 N/m. The free-stream velocity is 30 m/s, and the density of air is 1.225 kg/m\(^3\). The circulation around the cylinder is \_\_\_\_ m\(^2\)/s (rounded off to two decimal places).
In a centrifugal compressor, the eye tip diameter is 10 cm. For a shaft rotational speed of 490 rotations per second, the tangential speed at the inducer tip is \_\_\_ m/s (rounded off to one decimal place).
An ideal two-stage rocket has identical specific impulse and structural coefficient for its two stages. For an optimized rocket, the two stages have identical payload ratio as well. The payload is 2 tons and the initial mass of the rocket is 200 tons. The mass of the second stage of the rocket (including the final payload mass) is \_\_\_\_ tons.
A gaseous fuel mixture comprising 3 moles of methane and 2 moles of ammonia is combusted in \( X \) moles of pure oxygen in stoichiometric amount. Assuming complete combustion, with only \( {CO}_2 \), \( {H}_2{O} \), and \( {N}_2 \) in the product gases, the value of \( X \) is \_\_\_. \[ 3 \, {CH}_4 + 2 \, {NH}_3 + X \, {O}_2 \rightarrow {Products (CO}_2, \, {H}_2{O}, \, {N}_2{)} \]
A simply supported horizontal beam is subjected to a distributed transverse load varying linearly from \( q_0 \) at A to zero at B, as shown in the figure. Which one of the following options is correct?
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A stress field is given by \( \sigma_{xx} = \sigma_{zz} = C_1 y \); \( \sigma_{yy} = C_2 y \); \( \tau_{xy} = \tau_{yz} = \tau_{zx} = 0 \), where \( C_1 \) and \( C_2 \) are non-zero constants. If the stress field satisfies equilibrium, which one of the following options is correct?
For a homogeneous, isotropic material, the relation between the shear modulus (\( G \)), Young’s modulus (\( E \)), and Poisson’s ratio (\( \nu \)) is \_\_\_\_?
A uniform symmetric cross-section cantilever beam of length \( L \) is subjected to a transverse force \( P \) at the free end, as shown in the figure. The Young’s modulus of the material is \( E \) and the moment of inertia is \( I \). Ignoring the contributions due to transverse shear, the strain energy stored in the beam is \_\_\_\_\_.
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To achieve longitudinal static stability of a general aviation airplane, which one of the following conditions should be satisfied?
In the given figure, plate ABCD in its undeformed configuration (solid line) is a rhombus with all the internal angles being 90°. The lengths of the undeformed diagonals are 20 cm. ABCD deforms as shown by the dotted lines. Upon deformation, diagonal AC reduces to 19.96 cm and BD increases to 20.04 cm. In the given x-y coordinate system, the engineering shear strain \( \gamma_{xy} \) is equal to \_\_\_\_\_.
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For a general aviation airplane, which one of the following has a destabilizing effect on its static roll stability?
A general aviation airplane is flying at an altitude of 5000 m. The indicated airspeed is 250 km/h. Assume that there are no instrument errors and position errors. Neglecting compressibility effects, which one of the following options is FALSE?
In a fluid flow, Mach number is an estimate of \_\_\_\_\_.
A positively cambered airfoil is placed in a uniform flow (velocity, \( U_\infty \)) at its zero-lift angle of attack. \( M \) is the corresponding pitching moment. Which one of the following representations accurately describes this scenario?
A general aviation airplane is in steady and level flight. The airplane is prone to adverse yaw. Which one of the following options best describes the deflections of aileron and rudder to achieve a coordinated right turn?
Consider a pair of point vortices with clockwise circulation \( \Gamma \) each. The distance between their centers is \( a \), as shown in the figure. Assume two-dimensional, incompressible, inviscid flow. Which one of the following options is correct?
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For a NACA 4415 airfoil, the location of maximum camber, as a fraction of the chord length from the leading edge, is \_\_\_\_\_\_.
For a two-dimensional incompressible flow over a flat plate, the laminar boundary layer thickness at a distance \( x \) from the leading edge is \( \delta \). If \( Re_x \) is the Reynolds number defined based on length scale \( x \), \[ \frac{\delta}{x} \propto \_\_\_\_\_\_. \]
If \( i = \sqrt{-1} \), \[ \frac{(i+1)^3}{i-1} = \_\_\_\_\_\_\_\_. \]
The partial differential equation \[ \frac{\partial^2 u}{\partial x^2} + 4 \frac{\partial^2 u}{\partial x \partial y} + 2 \frac{\partial^2 u}{\partial y^2} = 0 \] is \_\_\_\_\_\_.
The eigenvalues of the matrix \[ \begin{bmatrix} 1 & 2
0 & 3 \end{bmatrix} \] are \_\_\_\_\_ .
Let the function \( f(x) \) be defined as: \[ f(x) = \begin{cases} A + x, & {if } x<2
1 + x^2, & {if } x \geq 2 \end{cases} \] If the function \( f(x) \) is continuous at \( x = 2 \), the value of \( A \) is \_\_\_\_\_.
For any real symmetric matrix \( A \), the transpose of \( A \) is \_\_\_\_ .