Aerospace Engineering Gate 2017 Questions with Answer

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Ques 27 GATE 2017

An aircraft wing is idealized as a cantilever beam of constant width and length I with a tip mass of weight W (Newtons) and has a uniformly distributed loading of q_o (Newtons/m) as shown in the figure. Flexural rigidity =EI and q_o l=10 W.

The upward deflection of the tip of the aircraft wing under the given loading can be expressed as:

δ=k Wl³/EI

The value of k is _______ (in three decimal places).

(0.910 to 0.920) is the correct answer.

Ques 28 GATE 2017

For the state of plane stress shown in the figure, the minimum principal stress is -7 MN/m² The normal stress σ_x in MN/m² is equal to _______ (round to nearest integer).

(104 to 106) is the correct answer.

Ques 29 GATE 2017

The maximum normal stress in MN/m² for the thin walled beam of square cross section of outer dimension 120 mm x 120 mm and wall thickness 1 mm under the action of moment M₀=96 Nm as shown in the figure is _______ (in three decimal places).

(6.900 to 7.400) is the correct answer.

Ques 30 GATE 2017

The idealized cross section of a thin-walled wing box structure shown in the figure is subjected to an anticlockwise torque of 10 kNm. The corresponding shear-flow distribution under this loading condition is shown in the figure. The area of each cell is A₁=300x10³mm² and A₂=250x10³mm².

The ratio of the unknowns x/y is given by _______ (in three decimal places).

(0.640 to 0.650) is the correct answer.

Ques 31 GATE 2017

A trace from the schlieren photograph of the flow around a corner reveals the edges of the expansion fan as shown below. The leading and trailing edges of the expansion fan make the angles as shown. Assuming γ=1.4 the angle of the expansion fan (in degrees) is _______ (in two decimal places)

Prandtl Meyer function is given by

ν(M)=√(γ+1/γ-1)tan^-1√((γ-1)/(γ+1)(M²-1))-tan^-1√(M²-1)

(48.00 to 49.00) is the correct answer.

Ques 32 GATE 2017

A strong normal shock wave, with a pressure ratio of 29 across it, is travelling into stationary air (γ=1.4) at T=280 K in a straight duct (see figure). The magnitude of the velocity of the air induced behind the shock wave is _______ m/s. (round to nearest integer)

(Gas constant =287 J/kg.K Shock wave relations:

Pressure ratio: p₂/p₁=1+(2γ/(γ+1))(M²-1); Density ratio: ρ₂/ρ₁=((y+1)M²)/((y-1)M²+2)

(1341 to 1343) is the correct answer.

Ques 33 GATE 2017

Given the vectors
and →v₂ is given by:
→v₁ = ℔ + 3∗ĵ
→v₂ = 2℔ - 4∗ĵ + 3k̂,
the vector →v₃ that is perpendicular to both →v₁ and →v₂ is given by:

→v₃ = →v₁ - (→v₁ ⋅ →v₂) →v₂/|→v₂|

→v₃ = ∗k̂

→v₃ = →v₂ - (→v₁ ⋅ →v₂) →v₁/|→v₁|

→v₃ = (→v₁ × →v₂) / |→v₁ × →v₂|

(d) is the correct answer.

Ques 34 GATE 2017

The value of the integral I = ∫_C((x-y)dx+x²dy) with C the boundary of the square 0≤x≤2; 0≤y≤2, is

(11.9) is the correct answer.

Ques 35 GATE 2017

Let →v(t) be a unit vector that is a function of the parameter t.
Then →v ⋅ d→v/dt =

(0) is the correct answer.

Ques 36 GATE 2017

The eigenvalues λ_n and eigenfunctions u_n(x) of the Sturm-Liouville problem d²y/dx² + k²λy=0 , 0

λ_n=n²π²; u_n(x)=sin λ_nx, n=0, ±1, ±2, ∙∙∙,∞

λ_n=n²π²/k²; u_n(x)=sin knπx, n=0, ±1, ±2, ∙∙∙,∞

λ_n=n²π²/k²; u_n(x)=sin nπx n=0, ±1, ±2, ∙∙∙,∞

λ_n=n²π²; u_n(x)=sin nπx, n=0, ±1, ±2, ∙∙∙,∞

Ques 37 GATE 2017

3-point Gaussian integration formula is given by:
∫_-1¹f(x)dx ≈ ∑_j=1³A_jf(x_j) with x₁=0, x₂=-x₃=-√(3/5); A₁=8/9 A₂=A₃=5/9
This formula exactly integrates