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Physics Resonance: Problem set 20 -->

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Sunday, 6 November 2016

Problem set 20

  1. Let v, p and E denote the speed, the magnitude of the momentum, and the energy of a free particle of rest mass m. Then
    1. dE/dp=constant
    2. p=mv
    3. v=cp/\sqrt{p^2+m^2c^2}
    4. E=mc^2
  2. A binary star system consists of two stars S_1 and S_2, with masses m and 2m, respectively, separated by a distance r. If both S_1 and S_2 individually follow circular orbits around the centre of mass with instantaneous speeds V_1 and V_2 respectively, the speeds ratio V_1/V_2 is
    1. \sqrt{2}
    2. 1
    3. 1/2
    4. 2
  3. Three charges are located on the circumference of a circle of radius R as shown in the figure below. The two charges Q subtend an angle 90^o at the centre of the circle. The charge q is symmetrically placed with respect to the charges Q. If the electric field at the centre of the circle is zero, what is the magnitude of Q?
    1. q/\sqrt{2}
    2. \sqrt{2}q
    3. 2q
    4. 2q
  4. Consider a hollow charged shell of inner radius a and outer radius b. The volume charge density is \rho(r) =\frac{k}{r^2} (k is a constant) in the region a < r < b. The magnitude of the electric field produced at distance r > a is
    1. \frac{k(b-a)}{\epsilon_0r^2} for all r > a
    2. \frac{k(b-a)}{\epsilon_0r^2} for a < r < b and \frac{kb}{\epsilon_0r^2} for r > b
    3. \frac{k(r-a)}{\epsilon_0r^2} for a < r < b and \frac{k(b-a)}{\epsilon_0r^2} for r > b
    4. \frac{k(r-a)}{\epsilon_0a^2} for a < r < b and \frac{k(b-a)}{\epsilon_0a^2} for r > b
  5. Consider the interference of two coherent electromagnetic waves whose electric field vectors are given by \vec E_1 = \hat i E_0 \cos{(\omega t+\phi)} and \vec E_2 = \hat j E_0 \cos{(\omega t+\phi)} where \phi is the phase difference. The intensity of the resulting wave is given by \frac{\epsilon_0}{2}\left < E^2\right >, where \left < E^2\right > is the time average of E^2. The total intensity is
    1. 0
    2. \epsilon_0E_0^2
    3. \epsilon_0E_0^2\sin^2{\phi}
    4. \epsilon_0E_0^2\cos^2{\phi}

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