Oscillations-Quiz-7

OSCILLATIONS QUIZ 7

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 of mass m=2 kg executes SHM in xy plane between points A and B under the action of force F ⃗=F_x i ̂+F_y J ̂. Minimum time taken by the particle to move from A to B is 1 s. At t=0 the particle is at x=2 and y=2. Then F_x, as function of time t is

•  a) -4π^2 sin⁡πt
•  b) -4π^2 cos⁡πt
•  c) 4π^2 cos⁡πt
•  d) None of these

Solution

Q2.The potential energy of a particle executing SHM along the x-axis is given by U=U_0-U_0 cos ax. What is the period of oscillation

•  2π√(ma/U_0 )
•  2π√(U_0/ma)
•  2π/a √(m/U_0 )
•  2π√(m/〖aU〗_0 )

Solution

Q3.  The number of independent constituent simple harmonic motions yielding a resultant displacement equation of the periodic motion as y=8 sin²⁡(t/2)sin⁡(10t) is

•  8
•  6
•  4
•  3

Solution

Q4. A cork floating on the pond water executes a single harmonic motion, moving up and down over a range of 4 cm. The time period of the motion is 1 s. At t=0, the cork is at its lowest position of oscillation, the position and velocity of the cork at t=10.5 s, would be

•  a) 2 cm above the mean position, 0 m/s
•  b) 2 cm below the mean position, m/s
•  c) 1 cm above the mean position, 2√3 π m/s up
•  d) 1 cm below the mean position, 2√3 π m/s up

Solution

Q5.If x,v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time?

•  a² T²+4π² v²
•  aT/x
•  aT+2πv
•  aT/v

Solution
 

Q6. A body of mass 100 g attached to a spring executes SHM of period 2 s and amplitude 10 cm. How long a time is required for it to move from a point 5 cm below its equilibrium position to a point 5 cm above it, when it makes simple harmonic vertical oscillations (take g=10 m/s²)?

•  0.6 s
•  1/3 s
•  1.5 s
•  2.2 s

Solution

Q7.A simple pendulum oscillates slightly above a large horizontal metal plate. The bob is given a charge. The time period

•  Has no effect, whatever be the nature of charge
•  Always decreases, whatever be the nature of charge
•  Always increases, whatever be the nature of charge
•  A increases or decreases depending upon the nature of charge

Solution

Q8.Figure shows the variation of force acting on a particle of mass 400 g executing simple harmonic motion the frequency of oscillation of the particle is

•  4s^-1
•  (5/2π) s^-1
•  (1/8π) s^-1
•  (1/2π) s^-1

Solution

Q9.The coefficient of friction between block of mass m and 2m is μ=2 tan⁡θ. There is no friction between block of mass 2m and inclined plane. The maximum amplitude of the two block system for which there is no relative motion between both the blocks is

•  g sin⁡θ √(k/m)
•  (mg sin⁡θ)/k
•  (3 mg sin⁡θ)/k
•  None of these

Solution

Q10. The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The amplitude of the point P is

•  (k₁ A)/k₂
•  (k₂ A)/k₁
•  (k₁ A)/k₁ + k₂
•  (k₂ A)/k₁ + k₂

Solution