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The potential energy of a particle movin...

The potential energy of a particle moving along x-axis is given by `U = 20 + 5 sin (4 pi x)`, where `U` is in `J` and `x` is in metre under the action of conservative force :

A

if total mechanical energy is `20 J`,
then at `x = 7//8 m`, particle is at equilibrium

B

if total mechanical energy is `20 J`,
then at `x = 7//8 m` particle is not at equilibrium

C

if total mechanical energy is `20 J`,
then at `x = 3//8 m`, particle is at equilibrium

D

if total mechanical energy is `20 J`,
then at `x = 3//8 m`, particle is not at equilibrium.

Text Solution

Verified by Experts

The correct Answer is:
A, C

`U_(min)` is at `sin(4 pix) = -1`
`U_(min) = 20 -5 = 15 J`
`K_(max) =E-U_(min) = 20 - 15 = 5 J`
`4 pi x=(3)/(2)pi,(7)/(2)p , x = (3)/(8),(7)/(8),....`.
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Knowledge Check

  • The potential energt of a particle of mass 0.1 kg, moving along the x-axis, is given by U=5x(x-4)J , where x is in meter. It can be concluded that

    A
    the particle is acted upon by a constant force
    B
    the speed of the particle is maximum at `x=2m`
    C
    the particle executes SHM
    D
    the period of oscillation of the particle `((pi)/(5))` s
  • The potential energy of a particle oscillating on x-axis is given as U +20 +(x-2)^(2) . The mean position is at

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    `x =2m`
    B
    `x =1m`
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  • The potential energy of a particle of mass 1kg in motion along the x- axis is given by: U = 4(1 - cos 2x) , where x in metres. The period of small oscillation (in sec) is

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