A mass $m=1.0 \mathrm{~kg}$ is put on a flat pan attached to a vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes simple harmonic motion. The spring constant is $500 \mathrm{~N} / \mathrm{m}$. What is the amplitude $\mathrm{A}$ of the motion, so that the mass $m$ tends to get detached from the pan ? (Take $g=10 \mathrm{~m} / \mathrm{s}^{2}$ ). The spring is stiff enough so that it does not get distorted during the motion.

Question:

A mass $m=1.0 \mathrm{~kg}$ is put on a flat pan attached to a vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes simple harmonic motion. The spring constant is $500 \mathrm{~N} / \mathrm{m}$. What is the amplitude $\mathrm{A}$ of the motion, so that the mass $m$ tends to get detached from the pan ?

(Take $g=10 \mathrm{~m} / \mathrm{s}^{2}$ ).

The spring is stiff enough so that it does not get distorted during the motion.

  1. $\mathrm{A}>2.0 \mathrm{~cm}$

  2. $\mathrm{A}=2.0 \mathrm{~cm}$

  3. $\mathrm{A}<2.0 \mathrm{~cm}$

  4. $\mathrm{A}=1.5 \mathrm{~cm}$

JEE Main Previous Year Single Correct Question of JEE Main from Physics Oscillations chapter.

JEE Main Previous Year Online April 22, 2013


Correct Option: 3

Solution:

Related Questions

  • The position co-ordinates of a particle moving in a 3-D coordinate system is given by

    $x=\mathrm{a} \cos \omega \mathrm{t}$

    $y=a \sin \omega t$

    and $z=a \omega t$

    The speed of the particle is:

    View Solution

  • TTwo simple harmonic motions, as shown, are at right angles. They are combined to form Lissajous figures.

    $$

    \begin{aligned}

    &x(t)=A \sin (a t+\delta) \\

    &y(t)=B \sin (b t)

    \end{aligned}

    $$

    Identify the correct match below

    View Solution

  • The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is $10 \mathrm{~s}^{-1}$. At, $\mathrm{t}=0$ the displacement is $5 \mathrm{~m}$. What is the maximum acceleration ? The initial phase is $\frac{\pi}{4}$

    View Solution

  • A particle performs simple harmonic mition with amplitude A. Its speed is trebled at the instant that it is at a distance $\frac{2 \mathrm{~A}}{3}$ from equilibrium position. The new amplitude of the motion is :

    View Solution

  • Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to $\mathrm{A}$ and $\mathrm{T}$, respectively. At time $\mathrm{t}=0$ one particle has displacement $A$ while the other one has displacement

    $\frac{-\mathrm{A}}{2}$ and they are moving towards each other. If they cross each other at time $\mathrm{t}$, then $\mathrm{t}$ is:

    View Solution

  • A simple harmonic oscillator of angular frequency $2 \mathrm{rad}$ $\mathrm{s}^{-1}$ is acted upon by an external force $\mathrm{F}=\sin t \mathrm{~N}$. If the oscillator is at rest in its equilibrium position at $t=0$, its position at later times is proportional to:

    View Solution

  • $x$ and $y$ displacements of a particle are given as $x(t)=a \sin$ $\omega t$ and $y(t)=a \sin 2 \omega t$. Its trajectory will look like :

    View Solution

  • A body is in simple harmonic motion with time period half second $(T=0.5 \mathrm{~s})$ and amplitude one $\mathrm{cm}(A=1 \mathrm{~cm})$. Find the average velocity in the interval in which it moves form equilibrium position to half of its amplitude.

    View Solution

  • Which of the following expressions corresponds to simple harmonic motion along a straight line, where $x$ is the displacement and $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are positive constants?

    View Solution

  • A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; $x=a_{1} \cos \omega t$ and $y=a_{2} \cos 2 \omega t$ traces a curve given by:

    View Solution

Leave a Reply

Your email address will not be published.

error: Content is protected !!
Download App