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GATE 2017-2018 :: GATE Mechanical

  1. Two large diffuse gray parallel plates, separated by a small distance, have surface temperatures of 400 K and 300 K. If the emissivities of the surfaces are 0.8 and the Stefan-Boltzmann constant is 5.67 * 10-8W/m2K4, the net radiation heat exchange rate in kW/m2 between the two plates is
  2. A.
    0.66
    B.
    0.79
    C.
    0.99
    D.
    3.96

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  3. A hinged gate of length 5 m, inclined at 30° with the horizontal and with water mass on its left, is shown in the figure below. Density of water is 1000 kg/m3. The minimum mass of the gate in kg per unit width (perpendicular to the plane of paper), required to keep it closed is

  4. A.
    5000
    B.
    6600
    C.
    7546
    D.
    9623

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  5. The pressure, temperature and velocity of air flowing in a pipe are 5 bar, 500 K and 50 m/s, respectively. The specific heats of air at constant pressure and at constant volume are 1.005 kJ/kgK and 0.718 kJ/kgK, respectively. Neglect potential energy. If the pressure and temperature of the surroundings are 1 bar and 300 K, respectively, the available energy in kJ/kg of the air stream is
  6. A.
    170
    B.
    187
    C.
    191
    D.
    213

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  7. The probability that a student knows the correct answer to a multiple choice question is 2/3. If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is 1/4. Given that the student has answered the question correctly, the conditional probability that the student knows the correct answer is
  8. A.
    2/3
    B.
    3/4
    C.
    5/6
    D.
    8/9

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  9. The solution to the differential equation d2u/dx2 - k du/dx = 0 where k is a constant, subjected to the boundary conditions u(0) = 0 and u(L) = U, is
  10. A.
    u = U x/L
    B.
    u = U[(1 - ekx)/(1 - ekL)]
    C.
    u = U[(1 - e-kx)/(1 - e-kL)]
    D.
    u = U[(1 + ekx)/(1 + ekL)]

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  11. The value of the definite integral  is
  12. A.
    4/9 √e3 + 2/9
    B.
    2/9 √e3 - 4/9
    C.
    2/9 √e3 + 4/9
    D.
    4/9 √e3 - 2/9

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  13. A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material details.

    width of the plate w = 200 mm, thickness of the plate t = 5 mm, number of rivets n = 3, diameter of the rivet dr = 10 mm, diameter of the rivet hole dh = 11 mm, allowable tensile stress of the plate σp = 200 MPa, allowable shear stress of the rivet σs = 100 MPa and allowable bearing stress of the rivet σc = 150 MPa. 
    If the rivets are to be designed to avoid crushing failure, the maximum permissible load P in kN is
  14. A.
    7.50
    B.
    15.00
    C.
    22.50
    D.
    30.00

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  15. A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material details.

    width of the plate w = 200 mm, thickness of the plate t = 5 mm, number of rivets n = 3, diameter of the rivet dr = 10 mm, diameter of the rivet hole dh = 11 mm, allowable tensile stress of the plate σp = 200 MPa, allowable shear stress of the rivet σs = 100 MPa and allowable bearing stress of the rivet σc = 150 MPa. 
    If the plates are to be designed to avoid tearing failure, the maximum permissible load P in kN is
  16. A.
    83
    B.
    125
    C.
    167
    D.
    501

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  17. Water (specific heat, cp = 4.18 kJ/kgK) enters a pipe at a rate of 0.01 kg/s and a temperature of 20°C. The pipe, of diameter 50 mm and length 3 m, is subjected to a wall heat flux qnw in W/m2:
    If qnw = 2500x, where x is in m and in the direction of flow (x = 0 at the inlet), the bulk mean temperature of the water leaving the pipe in °C is
  18. A.
    42
    B.
    62
    C.
    74
    D.
    104

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  19. Water (specific heat, cp = 4.18 kJ/kgK) enters a pipe at a rate of 0.01 kg/s and a temperature of 20°C. The pipe, of diameter 50 mm and length 3 m, is subjected to a wall heat flux qnw in W/m2:
    If qnw = 5000 and the convection heat transfer coefficient at the pipe outlet is 1000 W/m2K, the temperature in °C at the inner surface of the pipe at the outlet is
  20. A.
    71
    B.
    76
    C.
    79
    D.
    81

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