Oscillations-Quiz-5

OSCILLATIONS QUIZ 5

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 thin–walled tube of mass m and radius R has a rod of mass m and very small cross section soldered on its inner surface. The side-view of the arrangement is as shown in the following figure. The entire arrangement is placed on a rough horizontal surface. The system is given a small angular displacement from its equilibrium position, as a result, the system performs oscillations. The time period of resulting oscillations if the tube rolls without slipping is

•  a) 2π√(4R/g)
•  b) 2π√(2R/g)
•  c) 2π√(R/g)
•  d) None of these

Solution

Q2.A particle executed S.H.M. starting from its mean position at t=0. If its velocity is √3 bω, when ω=2π/T, the time taken by the particle to move from b to the extreme position on the same side is

•  5π/6ω
•  π/3ω
•  π/2ω
•  π/4ω

Solution

Q3.  A wire is bent at an angle θ. A rod of mass m can slide along the bended wire without friction as shown in figure. A soap film is maintained in the frame kept in a vertical position and the rod is in equilibrium as shown in the figure. If rod is displaced slightly in vertical direction, then the time period of small oscillation of the rod is

•   2π√(l/g)
•  2π√((l cos⁡θ)/g)
•  2π√(l/(g cos⁡θ ))
•  2π√(l/(g tan⁡θ ))

Solution

Q4. A metre stick swinging in vertical plane about a fixed horizontal axis passing through its one end undergoes small oscillation of frequency f_0. If the bottom half of the stick were cut off, then its new frequency of small oscillation would become

•  a) f₀
•  b) √2 f₀
•  c) 2f₀
•  d) 2√2 f₀

Solution

Q5.An object of mass 0.2 kg executes simple harmonic motion along the x-axis with a frequency of 25/π Hz. At the position x=0.04 m, the object has a kinetic energy of 0.5 J and potential energy of 0.4 J. The amplitude of oscillation is

•  0.05 m
•  0.06 m
•  0.01 m
•  None of these

Solution
 

Q6. A particle is performing SHM with amplitude a and time period T. Its acceleration f varies with time as shown in figure. If at time t, kinetic energy of the particle is K, which of the following graphs is correct?

•  
  
•  
  
•  
  
•  
  

Solution

Q7.A certain simple harmonic vibrator of mass 0.1 kg has a total energy of 10 J. Its displacement from the mean position is 1 cm when it has equal kinetic and potential energies. The amplitude A and frequency n of vibration of the vibrator are

•  A=√2 cm, n=500/π Hz
•  A=√2 cm, n=1000/π Hz
•  A=1/√2 cm, n=500/π Hz
•  A=1/√2 cm, n=1000/π Hz

Solution

Q8.Two spring with negligible masses and force constants k_1=200N/m are attached to the block of mass m=10 kg as shown in the figure. Initially the block is at rest, at the equilibrium position in which both springs are neither stretched nor compressed. At time t=0, sharp impulse of 50 Ns is given to the block with a hammer along the spring

•  Period of oscillations for the mass m is π/6 s
•  Maximum velocity of the mass m during its oscillation is 10 m/s
•  Data are insufficient to determine maximum velocity
•  Amplitude of oscillation is 0.83 m

Solution

Q9.The instantaneous displacement x of a particle executing simple harmonic motion is given by x=a₁ sin⁡[ωt]+a₂ cos⁡[ωt+π/6]. The amplitude A of oscillation is given by

•  √(a_1^2+a_2^2+2a_1 a_2 cos⁡〖π/6〗 )
•  √(a_1^2+a_2^2+2a_1 a_2 cos⁡〖π/3〗 )
•  √(a_1^2+a_2^2-2a_1 a_2 cos⁡〖π/6〗 )
•  √(a_1^2+a_2^2-2a_1 a_2 cos⁡〖π/3〗 )

Solution

Q10. A block of mass 10 kg is in equilibrium as shown in figure. Initially the springs have same stretch. If the block is displaced in vertical direction by a small amount, then the angular frequency of resulting motion is (assume strings are never slack)

•  10√2
•  10√5
•  5√2
•  5√5

Solution