Oscillations (SHM) · JEE Main previous year questions

2022 18 questions

1. Q392022 · 29 Jul 2022 · Shift 1

   The time period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination $\alpha$, is given by :

   1. A.$2\pi \sqrt{\mathrm{L}/(\mathrm{g}\cos \alpha )}$
   2. B.$2\pi \sqrt{\mathrm{L}/(\mathrm{g}\sin \alpha )}$
   3. C.$2\pi \sqrt{\mathrm{L}/\mathrm{g}}$
   4. D.$2\pi \sqrt{\mathrm{L}/(\mathrm{g}\tan \alpha )}$
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   Answer: A

2. Q562022 · 29 Jul 2022 · Shift 2· Numerical answer

   The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is $10\mathrm{s}$. If the metallic bob is immersed in water, then the new time period becomes $5\sqrt{x}\mathrm{s}$. The value of $x$ will be ____.

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   Answer: 5

3. Q362022 · 28 Jul 2022 · Shift 2

   Assume there are two identical simple pendulum clocks. Clock - 1 is placed on the earth and Clock - 2 is placed on a space station located at a height h above the earth surface. Clock - 1 and Clock - 2 operate at time periods $4\text{ s}$ and $6\text{ s}$ respectively. Then the value of h is - (consider radius of earth $R_E=6400\text{ km}$ and $g$ on earth $10{\text{ m/s}}^2$ )

   1. A.$1200\text{ km}$
   2. B.$1600\text{ km}$
   3. C.$3200\text{ km}$
   4. D.$4800\text{ km}$
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   Answer: C

4. Q452022 · 28 Jul 2022 · Shift 2

   Sun light falls normally on a surface of area $36{\text{ cm}}^2$ and exerts an average force of $7.2\times 10^{-9}\text{ N}$ within a time period of 20 minutes. Considering a case of complete absorption, the energy flux of incident light is

   1. A.$25.92\times 10^2{\text{ W/cm}}^2$
   2. B.$8.64\times 10^{-6}{\text{ W/cm}}^2$
   3. C.$6.0{\text{ W/cm}}^2$
   4. D.$0.06{\text{ W/cm}}^2$
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   Answer: D

5. Q552022 · 28 Jul 2022 · Shift 2· Numerical answer

   The potential energy of a particle of mass $4\text{ kg}$ in motion along the x-axis is given by $U=4(1-\cos 4x)\text{ J}$. The time period of the particle for small oscillation ($\sin \theta \simeq \theta$) is $(\frac{\pi }{K})s$. The value of $K$ is _________.

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   Answer: 2

6. Q602022 · 28 Jul 2022 · Shift 2· Numerical answer

   In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of $0.5\text{ s}$ is measured from time of 100 oscillation with a watch of $1\text{ s}$ resolution. If measured value of length is $10\text{ cm}$ known to $1\text{ mm}$ accuracy, The accuracy in the determination of g is found to be $x\%$. The value of $x$ is _________.

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   Answer: 5

7. Q402022 · 27 Jul 2022 · Shift 1

   Two identical positive charges $Q$ each are fixed at a distance of '2a' apart from each other. Another point charge $q_0$ with mass 'm' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge $q_0$ executes SHM. The time period of oscillation of charge $q_0$ will be :

   1. A.$\sqrt{\frac{4{\pi }^3{\epsilon }_{0}m{a}^3}{q_{0}Q}}$
   2. B.$\sqrt{\frac{q_{0}Q}{4{\pi }^3{\epsilon }_{0}m{a}^3}}$
   3. C.$\sqrt{\frac{2{\pi }^2{\epsilon }_{0}m{a}^3}{q_{0}Q}}$
   4. D.$\sqrt{\frac{8{\pi }^3{\epsilon }_{0}m{a}^3}{q_{0}Q}}$
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   Answer: A

8. Q572022 · 27 Jul 2022 · Shift 1· Numerical answer

   A mass $0.9\text{ kg}$, attached to a horizontal spring, executes SHM with an amplitude $A_1$. When this mass passes through its mean position, then a smaller mass of $124\text{ g}$ is placed over it and both masses move together with amplitude $A_2$. If the ratio $\frac{A_1}{A_2}$ is $\frac{\alpha }{\alpha -1}$, then the value of $\alpha$ will be _________.

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   Answer: 16

9. Q402022 · 26 Jul 2022 · Shift 1

   When a particle executes Simple Harmonic Motion, the nature of graph of velocity as a function of displacement will be :

   1. A.Circular
   2. B.Elliptical
   3. C.Sinusoidal
   4. D.Straight line
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   Answer: B

10. Q412022 · 25 Jul 2022 · Shift 2

    The length of a seconds pendulum at a height $h=2R$ from earth surface will be: (Given $R$ = Radius of earth and acceleration due to gravity at the surface of earth, $g={\pi }^2{\text{ ms}}^{-2}$)

    1. A.$\frac{2}{9}\text{ m}$
    2. B.$\frac{4}{9}\text{ m}$
    3. C.$\frac{8}{9}\text{ m}$
    4. D.$\frac{1}{9}\text{ m}$
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    Answer: D

11. Q602022 · 25 Jul 2022 · Shift 2· Numerical answer

    Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the $\sqrt{3}$ times of amplitude of individual motions. The phase difference between the two motions is ___________ (degree).

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    Answer: 60

12. Q452022 · 27 Jun 2022 · Shift 1

    The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is :

    1. A.6 s
    2. B.8 s
    3. C.12 s
    4. D.36 s
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    Answer: D

13. Q572022 · 27 Jun 2022 · Shift 1· Numerical answer

    A pendulum of length $2\mathrm{m}$ consists of a wooden bob of mass $50\mathrm{g}$. A bullet of mass $75\mathrm{g}$ is fired towards the stationary bob with a speed $v$. The bullet emerges out of the bob with a speed $\frac{v}{3}$ and the bob just completes the vertical circle. The value of $v$ is ____ $\mathrm{m}{\mathrm{s}}^{-1}$. (if $g=10m/{\mathrm{s}}^2$).

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    Answer: 10

14. Q402022 · 27 Jun 2022 · Shift 2

    The equation of a particle executing simple harmonic motion is given by $x=\sin \pi \left(t+\frac{1}{3}\right)m$. At $t=1\text{s}$, the speed of particle will be (Given : $\pi =3.14$)

    1. A.$0{\text{ cm s}}^{-1}$
    2. B.$157{\text{ cm s}}^{-1}$
    3. C.$272{\text{ cm s}}^{-1}$
    4. D.$314{\text{ cm s}}^{-1}$
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    Answer: B

15. Q542022 · 27 Jun 2022 · Shift 2· Numerical answer

    A particle executes simple harmonic motion. Its amplitude is 8 cm and time period is 6 s. The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is ___________ s.

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    Answer: 1

16. Q372022 · 26 Jun 2022 · Shift 1

    Time period of a simple pendulum in a stationary lift is 'T'. If the lift accelerates with $\frac{g}{6}$ vertically upwards then the time period will be : (Where g = acceleration due to gravity)

    1. A.$\sqrt{\frac{6}{5}}T$
    2. B.$\sqrt{\frac{5}{6}}T$
    3. C.$\sqrt{\frac{6}{7}}T$
    4. D.$\sqrt{\frac{7}{6}}T$
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    Answer: C

17. Q492022 · 26 Jun 2022 · Shift 2

    The positive feedback is required by an amplifier to act an oscillator. The feedback here means :

    1. A.External input is necessary to sustain ac signal in output.
    2. B.A portion of the output power is returned back to the input.
    3. C.Feedback can be achieved by LR network.
    4. D.The base-collector junction must be forward biased.
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    Answer: B

18. Q352022 · 24 Jun 2022 · Shift 2

    Two massless springs with spring constants 2 k and 9 k, carry 50 g and 100 g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be :

    1. A.1 : 2
    2. B.3 : 2
    3. C.3 : 1
    4. D.2 : 3
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    Answer: B