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Physics Resonance: Problem set 4 -->

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Monday, 3 October 2016

Problem set 4

  1. For a system performing small oscillations, which of the following statement is correct?
    1. The number of normal modes and the number of normal coordinates is equal
    2. The number of normal modes is twice the number of normal coordinates
    3. The number of normal modes is half the number of normal coordinates
    4. There is no specific relationship between the number of normal modes and the number of normal coordinates
  2. For any process, the second law of thermodynamics requires that the change of entropy of the universe be
    1. Positive only
    2. Positive or zero
    3. Zero only
    4. Negative or zero
  3. A body of mass M=m_1+m_2 at rest splits into two parts of masses m_1 and m_2 by an internal explosion which generates a kinetic energy E. The speed of mass m_2 relative to mass m_1 is
    1. \sqrt{\frac{E}{m_1m_2}}
    2. \sqrt{\frac{2E}{m_1m_2}}
    3. \sqrt{\frac{EM}{m_1m_2}}
    4. \sqrt{\frac{2EM}{m_1m_2}}
  4. The value of x=1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\dots} }}
    1. \sqrt{2}
    2. 1.6
    3. \sqrt{3}
    4. 0.8
  5. In Young's double slit experiment, if one of the following parameters (\lambda, d and D) is increased in the same order keeping the other two same, then the fringe width
    1. decreases, decreases, increases
    2. decreases, increases, increases
    3. increases, decreases, increases
    4. increases, increases, decreases
  6. Ideal Atwood machine is nothing but an inextensible string of negligible mass going around the fixed pulley with masses m_1 and m_2 attached to the ends of the string. If m_1>m_2, then the magnitude of acceleration of mass m_1 is
    1. \frac{m_1g}{(m_1+m_2)}
    2. \frac{m_2g}{(m_1+m_2)}
    3. \frac{(m_1-m_2)g}{(m_1+m_2)}
    4. g
  7. A particle of mass m is released from a large height. Resistive force is directly proportional to velocity \bar v with k as a constant of proportionality. Asymptotic value of the velocity of particle is
    1. \frac{g}{k}
    2. \frac{k}{m}
    3. \frac{mg}{k}
    4. \frac{g}{km}
  8. The momentum of an electron (rest mass m_0), which has the same kinetic energy as its rest mass energy, is
    1. m_0c
    2. \sqrt{2}m_0c
    3. \sqrt{3}m_0c
    4. 2m_0c
  9. A planet of mass m moves around the in an elliptic orbit. If L denotes the angular momentum of the planet, then the rate at which area is swept by the radial vector is
    1. \frac{L}{2m}
    2. \frac{L}{m}
    3. \frac{2L}{2}
    4. \frac{\sqrt{2}L}{m}
  10. The matrix \begin{pmatrix}8&x&0\\4&0&2\\12&6&0\end{pmatrix} will become singular if the value of x is
    1. 4
    2. 6
    3. 8
    4. 12

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