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GATE 2017-2018 :: GATE Physics

  1. A uniform circular disk of radius R and mass M is rotating with angular speed w about an axis, passing through its center and inclined at an angle 60 degrees with respect to its symmetry axis. The magnitude of the angular momentum of the disk is,
  2. A.
    √3/4 wMR2
    B.
    √3/8 wMR2
    C.
    √7/8 wMR2
    D.
    √7/4 wMR2

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  3. Consider two small blocks, each of mass M, attached to two identical springs. One of the springs is attached to the wall, as shown in the figure. The spring constant of each spring is k. The masses slide along the surface and the friction is negligible. The frequency of one of the normal modes of the system is,

  4. A.
    √(3 + √2)/2 √k/M
    B.
    √(3 + √3)/2 √k/M
    C.
    √(3 + √5)/2 √k/M
    D.
    √(3 + √6)/2 √k/M

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  5. A charge distribution has the charge density given by ρ = Q{δ(x - x0) - δ(x + x0)}. For this charge distribution the electric field at (2x0, 0,0)
  6. A.
    2Qx/9πϵ0x02
    B.
    Qx/4πϵ0x03
    C.
    Qx/4πϵ0x02
    D.
    Qx/16πϵ0x02

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  7. A monochromatic plane wave at oblique incidence undergoes reflection at a dielectric interface. If  are the unit vectors in the directions of incident wave, reflected wave and the normal to the surface respectively, which one of the following expressions is correct?
  8. A.
    .

    B.
    .

    C.
    .

    D.
    .

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  9. In a normal Zeeman effect experiment, spectral splitting of the line at the wavelength 643.8 nm corresponding to the transition 5 1D2 → 5 1P1 of cadmium atoms is to be observed. The spectrometer has a resolution of 0.01 nm. The minimum magnetic field needed to observe this is 
    (me = 9.1 * 10-31 kg, e = 1.6 * 10-19C, c = 3 * 108 m/s)
  10. A.
    0.26 T
    B.
    0.52 T
    C.
    2.6 T
    D.
    5.2 T

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  11. The spacing between vibrational energy levels in CO molecule is found to be 8.44 * 10-2 eV. Given that the reduced mass of CO is 1.14 * 10-26 kg, Planck's constant is 6.626 * 10-34 Js and 1eV = 1.6 * 10-19 J. The force constant of the bond in CO molecule is

  12. A.
    1.87 N/m
    B.
    18.7 N/m
    C.
    187 N/m
    D.
    1870 N/m

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  13. A lattice has the following primitive vectors  . The reciprocal lattice corresponding to the above lattice is
  14. A.
    BCC lattice with cube edge of (Ï€/2) 
    B.
    BCC lattice with cube edge of (2Ï€) 
    C.
    FCC lattice with cube edge of (Ï€/2) 
    D.
    FCC lattice with cube edge of (2Ï€) 

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  15. The total energy of an ionic solid is given by an expression E = - α e2/4πϵ0r + B/r9 where α is Madelung constant, r is the distance between the nearest neighbours in the crystal and B is a constant. If r0 is the equilibrium separation between the nearest neighbours then the value of B is
  16. A.
    (α e2r08)/(36πϵ0)
    B.
    (α e2r08)/(4πϵ0)
    C.
    (2α e2r010)/(9πϵ0)
    D.
    (α e2r010)/(36πϵ0)

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  17. A proton is confined to a cubic box, whose sides have length 10-12 m. What is the minimum kinetic energy of the proton? The mass of proton is 1.67 * 10-27 kg and Planck's constant is 6.63 * 10-34 Js.
  18. A.
    1.1 * 10-17 J
    B.
    3.3 * 10-17 J
    C.
    9.9 * 10-17 J
    D.
    6.6 * 10-17 J

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  19. For the function f(z) = 16z/(z+3)(z-1)2, the residue at the pole z = 1 is (your answer should be an integer) ___________.
  20. A.
    3
    B.
    4
    C.
    5
    D.
    6

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