- Which one of the following engines should be used by a subsonic passenger transport airplane for minimum specific fuel consumption?
- Turbojet engine with after burner
- Turbofan engine
- Ramjet engine
- Scramjet engine

Answer:- Turbofan engine

SFC in increasing order:- (1)Turbofan (2)Turbojet with after burner (3)Ramjet (4)Scramjet - A spring-mass-damper system with a mass of 1 kg is found to have a damping ratio of 0.2 and a natural frequency of 5 rad/s. The damping of the system is given by
- 2 Ns/m
- 2 N/s
- 0.2 kg/s
- 0.2 N/s

Answer:- 2 Ns/m

*m = 1 kg*

*ζ = 0.2*

*ω*_{0}= 5 rad/s

*ω*_{0}= (k/m)^{1/2}⇒ k = mω_{0}^{2}⇒ k = 25 kg/s^{2}

*ζ = c/{2(mk)*^{1/2}} ⇒ c = 2ζ(mk)^{1/2}⇒ c = 2 kg/s = 2 Ns/m - If
*f(θ) =, then f(α)f(β) =**f(α/β)**f(α+β)**f(α-β)*- 2 x 2 zero matrix

*= f(α+β)* - An artificial satellite remains in orbit and does not fall to the earth because
- the centrifugal force acting on it balances the gravitational attraction
- the on-board rocket motors provide continuous boost to keep it in orbit
- its transverse velocity keeps it from hitting the earth although it falls continuously
- due to its high speed it derives sufficient lift from the rarefied atmosphere

Answer:- its transverse velocity keeps it from hitting the earth although it falls continuously

- The Euler iteration formula for numerically integrating a first order nonlinear differential equation of the form
*= f(x)*, with a constant step size of*Δt is**x*_{k+1}= x_{k}−Δt*f(x_{k})*x*_{k+1}= x_{k}+(Δt^{2}/2)*f(x_{k})*x*_{k+1}= x_{k}−(1/Δt)*f(x_{k})*x*_{k+1}= x_{k}+Δt*f(x_{k})

Answer:-

*x*_{k+1}= x_{k}+Δt*f(x_{k}) - The number of natural frequencies of an elastic beam with cantilever boundary conditions is
- 1
- 3
- 1000
- Infinite

Answer:-

- For maximum range of a glider, which one of the following conditions is true?
- lift to drag ratio is maximum
- rate of descent is minimum
- descent angle is maximum
- lift to weight ratio is maximum

Answer:- lift to drag ratio is maximum

**Maximum endurance**for a**reciprocating engine, propeller driven**airplane requires**lowest SFC**and**maximum C**_{L}^{3/2}/C_{D}**Maximum range**for a**reciprocating engine, propeller driven**airplane requires**lowest possible SFC**and**maximum C**_{L}/C_{D}**Maximum endurance**for a**jet**airplane requires**minimum TSFC**and**maximum****C**_{L}/C_{D}**Maximum range**for a**jet**airplane requires**minimum TSFC**and**maximum C**_{L}^{1/2}/C_{D}

- An airplane with a larger wing as compared to a smaller wing will necessarily have
- more longitudinal static stability
- less longitudinal static stability
- same longitudinal static stability
- more longitudinal static stability for an aft tail airplane if aerodynamic center of the larger wing is behind the center of gravity of the airplane

Answer:-

- The minimum value of
*J(x) = x*occurs at^{2}−7x+30*x = 7/2**x = 7/30**x = 30/7**x = 30*

Answer:-

*x = 7/2*

*J(x) = x*^{2}−7x+30

⇒*J'(x) = 2x−7*

⇒*J”(x) = 2*

⇒ minimum value occurs when*J'(x) = 2x−7 = 0*⇒*x = 7/2* - Two airplanes are identical except for the location of the wing. The longitudinal static stability of the airplane with low wing configuration will be
- more than the airplane with high wing configuration
- less than the airplane with high wing configuration
- same as the airplane with high wing configuration
- more if elevator is deflected

Answer:-

# GATE 2007 AEROSPACE ENGINEERING (Q 1-10)

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For answer to Q.4, centrifugal force balance gravitation pull.

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will you please explain how it is correct?

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