Oscillations-Quiz-3

OSCILLATIONS QUIZ - 3

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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

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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   7} ⁄ ₉
•  cos^{-1   5} ⁄ ₉
•  cos^{-1   4} ⁄ ₉
•  cos^{-1   1} ⁄ ₉

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

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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/s2 
•  5/π m and 5π/5 m/s2 
•  10/π m and 5π/2 m/s2 
•  5/π m and 5π/4 m/s2 

Solution

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