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OSCILLATIONS QUIZ - 3

Dear Readers,

JEE Advanced Physics Syllabus can be referred by the IIT aspirants to get a detailed list of all topics that are important in cracking the entrance examination. JEE Advanced syllabus for Physics has been designed in such a way that it offers very practical and application-based learning to further make it easier for students to understand every concept or topic by correlating it with day-to-day experiences. In comparison to the other two subjects, the syllabus of JEE Advanced for physics is developed in such a way so as to test the deep understanding and application of concepts..

Q1. A particle executing SHM of amplitude ‘a’ has a displacement a/2 at t=T/4 and a negative velocity. The epoch of the particle is
  •  π/3
  •  2π/3
  •  π
  •  5π/3
Solution
Q2.A physical pendulum is positioned so that its centre of gravity is above the suspension point. When the a pendulum is released it passes the point of stable equilibrium with an angular velocity ω. The period of small oscillations of the pendulum is
  •  4π/ω
  •  2π/ω
  •  π/ω
  •  π/2ω
Solution
Q3.  A particle of mass m is present in a region where the potential energy of the particle depends on the x-coordinate according to the expression U=a/x^2 -b/x, where a and b are positive constants. The particle will perform
  •  Oscillatory motion but not simple harmonic motion about its mean position for small displacements
  •  Simple harmonic motion with time period 2π√((8a^2 m)/b^2 ) about its mean position for small displacements
  •  Neither simple harmonic motion nor oscillatory about its mean position for small displacements
  •  None of the above
Solution

Q4. A mass m is suspended from a spring of force constant k and just touches another identical spring fixed to the floor as shown in the figure. The time period of small oscillations is
  •  2π√(m/k)
  •  π√(m/k+π) √(m/(k/2))
  •  π√(m/(3k/2))
  •  π√(m/k)+π√(m/2k)
Solution
Q5.A block of mass m is suspended from the ceiling of an elevator (at rest) through a light spring of spring constant k. Suddenly, the elevator starts falling down with acceleration g. Then
  •  The block executes simple harmonic motion with time period 2π√(m/k)
  •  The block executes simple harmonic motion with amplitude mg/k
  •  The block executes simple harmonic motion about its mean position and the mean position is the position when the spring acquires its natural length
  •  All of the above
Solution
Q6. The string of a simple pendulum is replaced by a uniform rod of length L and mass M while the bob has a mass m. It is allowed to make small oscillations. Its time period is
  •  

  •  
  •  
  •  
Solution





Q7. Two particles move parallel to the x-axis about the origin with same amplitude ‘a’ and frequency ω. At a certain instant they are found at a distance a /3 from the origin on opposite sides but their velocities are in the same direction. What is the phase difference between the two?
  •  cos-1   79
  •  cos-1   59
  •  cos-1   49
  •  cos-1   19
Solution





Q8. A particle performs SHM of amplitude A along a straight line. When it is at a distance 3/2 A from mean position, its kinetic energy gets increased by an amount 1/2mω2A2 due to an impulsive force. Then its new amplitude becomes
  •  

  •  
  •  
  •  

Solution







Q9. The following figure shows the displacement versus time graph for two particles A and B executing simple harmonic motions. The ratio of their maximum velocities is


  •  3:1
  •  1:3
  •  1:9
  •  9:1
  • Solution







    Q10. In problem 9, the maximum displacement and acceleration of the particle are respectively:
    •  10/π m and 5π m/s
    •  5/π m and 5π/5 m/s
    •  10/π m and 5π/2 m/s
    •  5/π m and 5π/4 m/s
    Solution





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