Home
Class 12
PHYSICS
A particle located in one dimensional po...

A particle located in one dimensional potential fold has potential energy function `U(x)=(a)/(x^(2))-(b)/(x^(3))`, where a and b are positive constants. The position of equilibrium corresponds to x =

A

`(3a)/(2b)`

B

`(2b)/(3a)`

C

`(2a)/(3b)`

D

`(3b)/(2a)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • RACE

    ALLEN|Exercise Basic Maths (CIRCULAR MOTION)|17 Videos
  • RACE

    ALLEN|Exercise Basic Maths (COLLISION AND CENTRE OF MASS )|12 Videos
  • RACE

    ALLEN|Exercise Basic Maths (FRICTION)|14 Videos
  • NEWTONS LAWS OF MOTION

    ALLEN|Exercise EXERCISE-III|28 Videos
  • SIMPLE HARMONIC MOTION

    ALLEN|Exercise Example|1 Videos

Similar Questions

Explore conceptually related problems

A particle located in one dimensional potential field has potential energy function U(x)=(a)/(x^(2))-(b)/(x^(3)) , where a and b are positive constants. The position of equilibrium corresponds to x equal to

A particle located in a one-dimensional potential field has its potential energy function as U(x)(a)/(x^4)-(b)/(x^2) , where a and b are positive constants. The position of equilibrium x corresponds to

A particle of mass m in a unidirectional potential field have potential energy U(x)=alpha+2betax^(2) , where alpha and beta are positive constants. Find its time period of oscillations.

A partical of mass m is located in a unidimensionnal potential field where potentical energy of the partical depends on the coordinates x as U (x) = (A)/(x^(2)) - (B)/(x) where A and B are positive constant. Find the time period of small oscillation that the partical perform about equilibrium possition.

A particle of mass m moves in a one dimensional potential energy U(x)=-ax^2+bx^4 , where a and b are positive constant. The angular frequency of small oscillation about the minima of the potential energy is equal to

A particle of mass m is located in a region where its potential energy [U(x)] depends on the position x as potential Energy [U(x)]=(a)/(x^2)-(b)/(x) here a and b are positive constants… (i) Write dimensional formula of a and b (ii) If the time perios of oscillation which is calculated from above formula is stated by a student as T=4piasqrt((ma)/(b^2)) , Check whether his answer is dimensionally correct.

A particle of mass m is located in a region where its potential energy [U(x)] depends on the position x as potential Energy [U(x)]=(a)/(x^2)-(b)/(x) here a and b are positive constants… (i) Write dimensional formula of a and b (ii) If the time perios of oscillation which is calculated from above formula is stated by a student as T=4piasqrt((ma)/(b^2)) , Check whether his answer is dimensionally correct.

A particle of mass m is moving in a potential well, for which the potential energy is given by U(x) = U_(0)(1-cosax) where U_(0) and a are positive constants. Then (for the small value of x)

If P.E. of a system is given by relation U= (A)/(x^(2))-(B)/(x) , where 'A'and'B' are positive constant, then the mean positive of S.H.M.is

The potential energy of a particle of mass 'm' situated in a unidimensional potential field varies as U(x) = U_0 [1- cos((ax)/2)] , where U_0 and a are positive constant. The time period of small oscillations of the particle about the mean position-

ALLEN-RACE-Basic Maths (WORK POWER & ENERGY)
  1. On a particle placed at origin a variable force F=-ax (where a is a po...

    Text Solution

    |

  2. The variation of potential energy U of a system is shown in figure. Th...

    Text Solution

    |

  3. A particle located in one dimensional potential fold has potential ene...

    Text Solution

    |

  4. A particle of mass m is taken from position A to position B along the ...

    Text Solution

    |

  5. The position (x) of a particle of mass 2 kg moving along x-axis at tim...

    Text Solution

    |

  6. The velocity (v) of a particle of mass m moving along x-axis is given ...

    Text Solution

    |

  7. A block of mass 8 kg is released from the top of an inclined smooth su...

    Text Solution

    |

  8. The position (x) of body moving along x-axis at time (t) is given by ...

    Text Solution

    |

  9. A block of mass m is released on the top of a smooth inclined plane of...

    Text Solution

    |

  10. A particle of mass 0.1 kg is subjected to a force which varies with di...

    Text Solution

    |

  11. An unloaded bus can be stopped by applying brakes on straight road aft...

    Text Solution

    |

  12. A body of mass m, accelerates uniformly from rest to V(1) in time t(1)...

    Text Solution

    |

  13. A car of mass m has an engine which can deliver power P, The minimum t...

    Text Solution

    |

  14. The rate of doing work by force acting on a particle moving along x - ...

    Text Solution

    |

  15. An object starts from rest and is acted upon by a variable force F as ...

    Text Solution

    |

  16. Which of the following force is not conservative :-

    Text Solution

    |

  17. A disc of mass m and radius r is free to rotate about its centre as sh...

    Text Solution

    |

  18. A particle of mass m is projected with speed u at an angle theta with ...

    Text Solution

    |

  19. A cubical block of mass m and edge a slides down a rough inclned plane...

    Text Solution

    |

  20. The torpue of force vecF=-2hati+2hatj+3hatk acting on a point vecr=hat...

    Text Solution

    |