Home
Class 12
PHYSICS
A particle is constrained to move in the...

A particle is constrained to move in the region `x ge 0` and its potential energy is given by
`U=2x^(4)-3x^(2)J` (where x is in m)
For what values of x, the particle is under
Stable equilibrium

Text Solution

Verified by Experts

`x=(sqrt(3))/(2)m`
Promotional Banner

Topper's Solved these Questions

  • WORK, POWER & ENERGY

    MOTION|Exercise Exercise - 1|42 Videos

  • WORK, POWER & ENERGY

    MOTION|Exercise Exercise - 2|30 Videos

  • WORK, POWER & ENERGY

    MOTION|Exercise SOLVED EXAMPLES|5 Videos

  • WAVES

    MOTION|Exercise EXERCISE -4 (Level -II) (previous year JEE Advanced)|10 Videos

Similar Questions

Explore conceptually related problems

A particle is constrained to move in the region x ge 0 and its potential energy is given by U=2x^(4)-3x^(2)J (where x is in m) For what values of x, the particle is under Unstable equilibrium

A single conservative force F(x) acts on a 1.0-kg particle that moves along the x-axis. The potential energy U(x) is given by U(x)=20+(x-2)^2 where x is in meters. At x=5.0m , the particle has a kinetic energy of 20J . The maximum and minimum values of x, respectively, are

A single conservative force F(x) acts on a 1.0-kg particle that moves along the x-axis. The potential energy U(x) is given by U(x)=20+(x-2)^2 where x is in meters. At x=5.0m , the particle has a kinetic energy of 20J . Determine the equation of F(x) as a function of x.

A particle free to move along the X- axis has potential energy given by U(X)=k[1-exp(-X^(2))] of appropriate dimensions. Then-

A single conservative force F(x) acts on a 1.0-kg particle that moves along the x-axis. The potential energy U(x) is given by U(x)=20+(x-2)^2 where x is in meters. At x=5.0m , the particle has a kinetic energy of 20J . The maximum kinetic energy of the particle and the value of x at which maximum kinetic energy occurs are

A single conservative force F(x) acts on a 1.0-kg particle that moves along the x-axis. The potential energy U(x) is given by U(x)=20+(x-2)^2 where x is in meters. At x=5.0m , the particle has a kinetic energy of 20J . What is the mechanical energy of a system?

A single conservative force F(x) acts on a on a (1.0kg ) particle that moves along the x-axis. The potential energy U(x) is given by: U(x) =20 + (x-2)^(2) where, x is meters. At x=5.0m the particle has a kinetic energy of 20J (a) What is the mechanical energy of the system? (b) Make a plot of U(x) as a function of x for -10mlexle10m , and on the same graph draw the line that represents the mechanical energy of the system. Use part (b) to determine. (c) The least value of x and (d) the greatest value of x between which the particle can move. (e) The maximum kinetic energy of the particle and (f) the value of x at which it occurs. (g) Datermine the equation for F(x) as a function of x. (h) For what (finite ) value of x does F(x) =0 ?.

A particle of mass m is executing oscillations about origin on the x axis amplitude A its potential energy is given as U(x) = beta x^(4) where beta is constant x cooridirate of the particle where the potential energy is one third of the kinetic energy is

A single conservative f_((x)) acts on a m = 1 kg particle moving along the x-axis. The potential energy U_((x)) is given by : U_((x)) = 20 + (x - 2)^(2) where x is in metres. At x = 5 m , a particle has kintetic energy of 20 J The maximum value of potential energy is:

A single conservative f_((x)) acts on a m = 1 kg particle moving along the x-axis. The potential energy U_((x)) is given by : U_((x)) = 20 + (x - 2)^(2) where x is in metres. At x = 5 m , a particle has kintetic energy of 20 J The maximum speed of the particle is:

MOTION-WORK, POWER & ENERGY -QUESTIONS FOR PRACTICE
  1. A skier starts from the top of a hill with speed 5m//s and slides down...

    Text Solution

    |

  2. An object of mass 4 kg moving along x-axis crosses origin with 4 m/s t...

    Text Solution

    |

  3. An object of mass 4 kg moving along x-axis crosses origin with 4 m/s t...

    Text Solution

    |

  4. Initially block shown is at rest and the spring is unstretched, when a...

    Text Solution

    |

  5. Initially block shown is at rest and the spring is unstretched, when a...

    Text Solution

    |

  6. In figure a spring with k = 168 N//m is in its relaxed length and is a...

    Text Solution

    |

  7. In figure a spring with k = 168 N//m is in its relaxed length and is a...

    Text Solution

    |

  8. A block of mass m = 2.0 kg is dropped from height h = 40 cm onto a spr...

    Text Solution

    |

  9. A chain of length L and mass Mis arranged as shown in following four c...

    Text Solution

    |

  10. A particle is constrained to move in the region x ge 0 and its potenti...

    Text Solution

    |

  11. A particle is constrained to move in the region x ge 0 and its potenti...

    Text Solution

    |

  12. A force F=-K(yhati+xhatj) (where K is a positive constant) acts on a p...

    Text Solution

    |

  13. A block starts from rest at point A , slides down a frictionless incl...

    Text Solution

    |

  14. A horse pulls a cart upto 200m in 5 minutes, exerting a force of 750N ...

    Text Solution

    |

  15. An 900-kg roller-coaster car is launched from a giant spring of consta...

    Text Solution

    |

  16. A small toy car of mass m slides with negligible friction on a ''loop'...

    Text Solution

    |

  17. A small toy car of mass m slides with negligible friction on a ''loop'...

    Text Solution

    |

  18. A small toy car of mass m slides with negligible friction on a ''loop'...

    Text Solution

    |

  19. A particle attached to a vertical string of length 1m is projected hor...

    Text Solution

    |

  20. A particle attached to a vertical string of length 1m is projected hor...

    Text Solution

    |