GATE 2007 AEROSPACE ENGINEERING (Q 31-40)

  1. The eigenvalues of the matrix A-1, where A = , are
    1. 1 and 1/2
    2. 1 and 1.3
    3. 2 and 3
    4. 1/2 and 1/3

    Answer:- 1/2 and 1/3
    Eigenvalues of A are 2 and 3. So, eigenvalues of A-1 are 1/2 and 1/3.

  2. The radius of the Earth is 6.37*106 m and the acceleration due to gravity at its surface is 9.81 m/s2. A satellite is in circular orbit at a height of 35.9*106m above the earth’s surface. This orbit is inclined at 10.5 degrees to the equator. The velocity change needed to make the orbit equatorial is:
    1. 561 m/s at 84.75 degrees to the initial direction
    2. 561 m/s at 95.25 degrees to the initial direction
    3. 281 m/s at 84.75 degrees to the initial direction
    4. 281 m/s at 95.25 degrees to the initial direction

    Answer:-

  3. A piston-prop airplane having propeller efficiency, ηp= 0.8 and weighing 73108 N could achieve maximum climb rate of 15 m/s at fight speed of 50 m/s. The excess Brake Power(BP) at the above flight condition will be
    1. 1700 kW
    2. 2100 kW
    3. 1371 kW
    4. 6125 kW

    Answer:- 1371 kW
    Rate of Climb(R/C) = Excess Power / Weight
    Therefore, Excess Power = 73108*15 = 1096620 W
    Therefore, Excess Brake Power = Excess Power / Propeller Efficiency = 1370775 W = 1371 kW

  4. An airplane model with a symmetric airfoil was tested in a wind tunnel. at angle of attack was estimated to be 0.08 and 0 respectively for elevator settings of 5 degrees up and 5 degrees down. The estimated value of the elevator control power of the model will be
    1. 0.07 per deg
    2. -1.065 per deg
    3. -0.008 per deg
    4. -0.762 per deg

    Answer:-

  5. The lateral-directional characteristic equation for an airplane gave the following set of roots:
  6. An airplane is flying at an altitude of 10 km above the sea level. Outside air temperature and density at 10 km altitude are 223 K and 0.413 kg/m3 respectively. The airspeed indicator of the airplane indicates a speed of 60 m/s. Density of air at sea level is 1.225 kg/m3 and value of gas constant R is 288 J/kg/K. The stagnation pressure(P0) measured by the Pitot tube mpounted on the wing tip ofr the airplane will be of magnitude
    1. 3.5*104 N/m2
    2. 2.0*104 N/m2
    3. 2.87*104 N/m2
    4. 0.6*104 N/m2

    Answer:- 2.87*104 N/m2
    The airspeed indicator shows equivalent airspeed. Therefore, sea level density is to be considered for velocity measurement.
    p = ρRT = 0.413*288*223 = 26525 N/m2
    0.5*ρs*v2 = 0.5*1.225*602 = 2205 N/m2
    Therefore, P0 = 26525+2205 = 28730 = 2.87*104 N/m2

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