Oscillations-Quiz-1

OSCILLATIONS QUIZ - 1

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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 spring balance has a scale that can read from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance when displaced and released oscillates harmonically with a time period of 0.6 s. The mass of the body is (take $d=\mathrm{10 }\mathrm{m}/{\mathrm{s^2}}^{}$)

•  10kg
•  25kg
•  18kg
•  22.8kg

Solution

Q2. Two particles P and Q describe SHM of same amplitude a and frequency v along the same straight line. The maximum distance between the two particles is. The initial phase difference between them is

•  0
•  $\pi /2$
•  $\pi /6$
•  $\pi /3$

Solution

Q3. A particle of mass m moving along the x -axis has a potential energy U(x) = a + bx² where a and b are positive constants. It will execute simple harmonic motion with a frequency determined by the value of

•  b alone
•  b and a alone
•  b and m alone
•  b, a and m alone

Solution

Q4. The time taken by a particle executing simple harmonic motion to pass from point A to B where its velocities are same, is 2 s. After another 2 s, it returns to (b). The time period of oscillation is

•  2 s
•  4 s
•  6 s
•  8 s

Solution

Q5. A block is resting on a piston which executes simple harmonic motion in vertical plain with a period of 2.0 s in vertical plane at an amplitude just sufficient for the block to separate from the piston. The maximum velocity of the piston is

•  $\frac{\mathrm{5/}}{\pi }\mathrm{m}/\mathrm{s}$
•  $\frac{\mathrm{10/}}{\pi }\mathrm{m}/\mathrm{s}$
•  $\frac{\mathrm{\pi /}}{2}\mathrm{m}/\mathrm{s}$
•  $\frac{\mathrm{20/}}{\pi }\mathrm{m}/\mathrm{s}$

Solution

Q6. A point mass is subjected to two simultaneous sinusoidal displacements in x - direction, $x_{\mathrm{1(t)}}\left( \right)=A\mathrm{sin }\omega t$ and $x_{\mathrm{2(}}\left(\mathrm{t)}\right)=A\sin (\left(\omega t+\frac{2\mathrm{\pi /}}{\mathrm{3)}}\right).$ Adding a third sinusoidal displacement $x_{\mathrm{3(}}\left(\mathrm{t)}\right)=B\sin (\omega t+\varphi )$ brings the mass to a complete rest. The values of B and ϕ

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Solution

Q7. A particle executing SHM has velocities u and v and accelerations a and b in two of its positions. Find the distance between these two positions

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Solution

Q8. Two masses m1 and m2 are suspended together by a massless spring of constant k. When the masses are in equilibrium, m1 is removed without disturbing the system; the amplitude of vibration is:

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•  T
  
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Solution

Q9. A metal rod of length L and mass m is pivoted at one end. A thin disk of mass M and radius R( < L) is attached at its centre to the free end of the rod. Consider two ways the disc is attached case A- the disc is not free to rotate about its centre and case B– the disc is free to rotate about its centre. The rod-disc system performs SHM in vertical plane after being released from the same displaced position. Which of the following statement(s) is/are true?

•  Restoring torque in case A = Restoring torque in case B
•  Restoring torque in case A < Restoring torque in case B
•  Angular frequency for case A < Angular frequency for case B
•  Angular frequency for case A  > Angular frequency for case B

Solution

Q10. A particle, free to move along the x-axis, has potential energy given by U_(x) = K[ 1 - exp(-x² ) for $-\infty <x<+\propto$ where k is a positive constant of appropriate dimensions. Then

•  For small displacement from x=0, the motion is simple harmonic
•  If its total mechanical energy is k/2 , it has its minimum kinetic energy at the origin
•  For any finite non-zero value of x, there is a force directed away from the origin
•  At points away from the origin, the particle is in unstable equilibrium

Solution