Home
Class 11
PHYSICS
The potential energy of a particle of ma...

The potential energy of a particle of mass 1 kg in a conservative field is given as `U=(3x^(2)y^(2)+6x)` J, where x and y are measured in meter. Initially particle is at (1,1) & at rest then:

A

Initial acceleration of particle is `6sqrt(5)ms^(2)`

B

Work done to slowly bring the particle to origin is 9 J

C

Work done to slowly bring the particle to origin is `-9` J

D

If particle is left free it moves in straight line

Text Solution

Verified by Experts

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

Topper's Solved these Questions

  • WORK, ENERGY AND POWER

    PHYSICS GALAXY - ASHISH ARORA|Exercise unsolvedMCQ|78 Videos
  • WORK, ENERGY AND POWER

    PHYSICS GALAXY - ASHISH ARORA|Exercise unsolved|1 Videos
  • WORK, ENERGY AND POWER

    PHYSICS GALAXY - ASHISH ARORA|Exercise Discussion Question|31 Videos
  • RIGID BODIES AND ROTATIONAL MOTION

    PHYSICS GALAXY - ASHISH ARORA|Exercise Unsolved Numerical|63 Videos

Similar Questions

Explore conceptually related problems

The potential energy of a particle of mass 5 kg moving in the x-y plane is given by U=(-7x+24y)J , where x and y are given in metre. If the particle starts from rest, from the origin, then the speed of the particle at t=2 s is

The potential energy of a particle under a conservative force is given by U ( x) = ( x^(2) -3x) J. The equilibrium position of the particle is at

Knowledge Check

  • The potential energy of a particle of mass 2 kg moving in a plane is given by U = (-6x -8y)J . The position coordinates x and y are measured in meter. If the particle is initially at rest at position (6, 4)m, then

    A
    Its acceleration is of magnitude 5 `m/s^2`
    B
    It crosses the y-axis at (x = 0, y = 6 m)
    C
    Its speed when it crosses the y-axis is 10 m/s
    D
    Both (1) & (3)
  • The potential energy of a particle of mass 1 kg moving in X-Y plane is given by U=(12x+5y) joules, where x an y are in meters. If the particle is initially at rest at origin, then select incorrect alternative :-

    A
    Magnitude of its acceleration is `13 m//s^(2)`
    B
    It never crosses y-axis
    C
    It never crosses x-axis
    D
    It moves in a circle.
  • The potential energy of particle of mass 1kg moving along the x-axis is given by U(x) = 16(x^(2) - 2x) J, where x is in meter. Its speed at x=1 m is 2 m//s . Then,

    A
    the motion of the particle is uniformly accelerated
    B
    the motion of the particle is periodic but not simple harmonic.
    C
    the motion of the particle is simple harmonic having equilibrium position at x=1m
    D
    kinetic energy of the particle is conserved
  • Similar Questions

    Explore conceptually related problems

    The potential energy of a partical of mass 2 kg moving in y-z plane is given by U=(-3y+4z)J where y and z are in metre. The magnitude of force ( in newton ) on the particle is :

    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

    The potential energy of a particle of mass 1 kg moving along x-axis given by U(x)=[(x^(2))/(2)-x]J . If total mechanical speed (in m/s):-

    The potential energy of a particle of mass 10 kg moving in XY-plane is given by U=(-7x+24y)J , where x and y are in metre. The particle is initially at the origin and moving with the speed (2.4hati+0.7hatj) . The force on the particle is

    The potential energy of a particle of mass 5 kg moving in xy-plane is given as U=(7x + 24y) joule, x and y being in metre. Initially at t=0 , the particle is at the origin (0,0) moving with velovity of (8.6hati+23.2hatj) ms^(1) , Then