## OSCILLATIONS QUIZ 4

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. One end and a spring of force constant K is fixed to a vertical cal wall and the other to a body of mass m resting on a smooth horizontal surface. There is another wall at a distance x_0 from the s body. The spring is then compressed by 3x_0 and released. The time taken to strick the wall from the instant of release is (given sin^(-1)⁡〖(1/3)=(Ï€/9〗)
•  a) Ï€/6 √(m/K)
•  b) 2Ï€/3 √(m/K)
•  c) Ï€/4 √(m/K)
•  d) 11Ï€/9 √(m/K)
Solution

Q2.A block of mass ‘m’ is suspended from a spring and executes vertical SHM of time period T as shown in figure. The amplitude to the SHM is A and spring is never in compressed state during the oscillation. The magnitude of minimum force exerted by spring on the block is
•  mg-(4Ï€^2)/T^2 mA
•  mg+(4Ï€^2)/T^2 mA
•  mg-Ï€^2/T^2 mA
•  mg+Ï€^2/T^2 mA
Solution

Q3.  A uniform stick of mass M and length L is pivoted at its centre. Its ends are tied to two springs each of force constant K. In the position shown in figure, the strings are in their natural length. When the string is displaced through a small angle Î¸ and released, the stick
•   Executes non-periodic motion
•  Executes periodic motion which is not simple harmonic
•  Executes SHM of frequency 1/2Ï€ √(6K/M)
•  Executes SHM of frequency 1/2Ï€ √(K/2M)
Solution

Q4. A particle of mass m is executing oscillations about the origin on the x-axis. Its potential energy is U(x)=k[x]^3, where k is a positive constant. If the amplitude of oscillation is a, then its time period T is
•  a) Proportional to 1/√a
•  b) Independent to a
•  c) Proportional to √a
•  d) Proportional to a^(3/2)
Solution

Q5.A block ‘A’ of mass m is placed on a smooth horizontal platform P and between two elastic massless spring S_1and S_2 fixed horizontally to two fixed vertical walls. The elastic constants of the two springs are equal to k and the equilibrium distance between the two springs both in relaxed states is d. The block is given a velocity v_0 initially towards one of the springs and it then oscillations and minimum separation d_m of the springs will be
•  T=2(d/v+Ï€√(m/k)),d_m=d
•  T=2(d/v+2Ï€√(m/k)),d_m=d-v√(m/k)
•  T=2(d/v+2Ï€√(m/k)),d_m=d-2v√(m/k)
•  T=2Ï€√(m/k),d_m=d
Solution

Q6. While a particle executes linear simple harmonic motion
•  Its linear velocity and acceleration pass through their maximum and minimum values once in each oscillation
•  Its linear velocity and acceleration pass through their maximum and minimum values twice in each oscillation
• Its linear velocity and acceleration pass through their maximum and minimum values four times in each oscillation
•  Its linear velocity and acceleration always attain their peak values simultaneously
Solution

Q7.A particle performing simple harmonic motion having time period 3 s is in phase with another particle which also undergoes simple harmonic motion at t=0. The time period of second particle is T (less than 3 s). If they are again in the same phase for the third time after 45 s, then the value of T will be
•  2.8 s
•  2.7 s
•  2.5 s
•  None of these
Solution

Q8.A body is performing simple harmonic motion with amplitude a and time period T. Variation of its acceleration (f) with time (t) is shown in figure. If at time t, velocity of the body is v, which of the following graphs is correct?
•
•
•
•
Solution

Q9.A soil cylinder of mass M and radius R is connected to a spring as shown in figure. The cylinder is placed on a rough horizontal surface. All the parts except the cylinder shown in the figure are alight. If the cylinder is displaced slightly from its mean position and released, so that it performs pure rolling back and forth about its equilibrium position, determine the time period of oscillation?
•  2Ï€√(M/k)
•  2Ï€√(3M/2k)
•  2Ï€√(3M/k)
•  None of these
Solution

Q10. A particle executes SHM with time period 8 s. Initially, it is at its mean position. The ratio of distance travelled by it in the 1st second to that in the 2nd second is
•  √2:1
•  1:(√2-1)
•  (√2+1):√2
• (√2-1):1
Solution

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