Home
Class 12
PHYSICS
When a particle is mass m moves on the x...

When a particle is mass `m` moves on the `x-` axis in a potential of the from `V(x) = kx^(2)`, it performs simple harmonic motion. The corresponding thime periond is proportional to `sqrt((m)/(k))`, as can be seen easily asing dimensional analysis. However, the motion of a pariticle can be periodic even when its potential enem increases on both sides `x = 0` in a way different from `kx^(2)` and its total energy is such that the particel does not escape to infinity. consider a particle of mass `m` moving onthe `x-`axis . Its potential energy is `V(x) = omega (alpha gt 0`) for `|x|` near the origin and becomes a constant equal to `V_(0)` for `|x| ge X_(0)` (see figure)

If the total energy of the particle is `E`, it will perform is periodic motion why if :

A

`E lt 0`

B

`E gt0`

C

`V_(0) gt E gt 0`

D

`E gt V_(0)`

Text Solution

Verified by Experts

The correct Answer is:
C
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • SIMPLE HARONIC MOTION

    MOTION|Exercise EXERCISE -4 (Leve-II)|8 Videos

  • SIMPLE HARMONIC MOTION

    MOTION|Exercise EXERCISE -3 Section - B Previous Year Problems | JEE MAIN|23 Videos

  • SOUND WAVES

    MOTION|Exercise Exercise - 3 (Section - B)|14 Videos

Similar Questions

Explore conceptually related problems

A particle moves on the x -axis according to the equation x=x_(0)sin2 omega t .The motion is simple harmonic ?

A particle moves on the X-axis according to the equation x=x_0 sin^2omegat . The motion simple harmonic

Knowledge Check

  • When a particle is mass m moves on the x- axis in a potential of the from V(x) = kx^(2) , it performs simple harmonic motion. The corresponding thime periond is proportional to sqrt((m)/(k)) , as can be seen easily asing dimensional analysis. However, the motion of a pariticle can be periodic even when its potential enem increases on both sides x = 0 in a way different from kx^(2) and its total energy is such that the particel does not escape to infinity. consider a particle of mass m moving onthe x- axis . Its potential energy is V(x) = alpha *x^4 (alpha gt 0 ) for |x| near the origin and becomes a constant equal to V_(0) for |x| ge X_(0) (see figure) If the total energy of the particle is E , it will perform is periodic motion why if :

    A
    `E lt 0`
    B
    `E gt 0`
    C
    `V_(0) gt E gt 0`
    D
    `E gt V_(0)`

  • When a particle of mass m moves on the X-axis in a potential of the form V(x) = kx^(2) , it performs simple harmonic motion. The corresponding time period is proportional to sqrt((m)/(k)) , as can be seen easily using dimensional analysis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of x = 0 in a way different from kx^(2) and its total energy is such that the particle does not escape to infinity. Consider a particle of mass m moving on the X-axis. Its potential energy is V(x) =a x^(2) (a gt 0) for |x| near the origin and becomes a constant equal to V_(0) for |x| ge X_(0) The acceleration of this particle for |X|>X_(0) is

    A
    proportional to `(v_(0)/(mX_(0)))`
    B
    propotinal to `sqrt(V_(0))/(mX_(0))`
    C
    proportional to `V_(0)`
    D
    Zero

  • When a particle of mass m moves on the X-axis in a potential of the form V(x) = kx^(2) , it performs simple harmonic motion. The corresponding time period is proportional to sqrt((m)/(k)) , as can be seen easily using dimensional analysis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of x = 0 in a way different from kx^(2) and its total energy is such that the particle does not escape to infinity. Consider a particle of mass m moving on the X-axis. Its potential energy is V(x) =a x^(2) (a gt 0) for |x| near the origin and becomes a constant equal to V_(0) for |x| ge X_(0) For periodic motion os small amplitude A . The time periodic T of this particle is proportional to

    A
    `Asqrt(m)/(alpha)`
    B
    `(1)/(A)sqrt(m)/(alpha)`
    C
    `Asqrt(alpha)/(m)`
    D
    `(1)/(A)sqrt(alpha)/(m)`

    • Similar Questions

    Explore conceptually related problems

    A particle moves on the X-axis according to the equation x=A+Bsinomegat . Let motion is simple harmonic with amplitude

    A body is performing simple harmonic motion. Then its

    A particle moves on the X- axis according to the equation x = x_(0) sin^(2)omegat . The motion is simple harmonic

    In simple harmonic motion, acceleration of the particle is zero, when its

    The potential energy of a particle, executing a simple harmonic motion, at a dis"tan"ce x from the equilibrium position is proportional to

    Home
    Profile