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

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

A

The velocity of the particle at `t=4s`, `5ms^(-1)`

B

The acceleration of the particle is `5ms^(-2)`.

C

The direction of motion of the particle initially (at t=0) is right angles to the direction of acceleration.

D

The path of the particle is circle.

Text Solution

Verified by Experts

The correct Answer is:
A, B
`F=-[(del)/(delX)hati + (delU)/(dely)hatj]=(7hati-24hatj) N`
`a=F/m =(7/5hati - (24)/5hatj)m//s`
`|a|=ssqrt((7/5)^(2) + (24/5)^(2) =5 m//s^(2))`
Since, `a="constant"`, we can apply,
`v=u+at`
`=(8.6hati + 23.2hatj) + (-7/5hati-(24)/5hatj)(4)`
`=(3hati +4hatj)m//s`
`|v|=sqrt((3)^(2) + (4)^(2)=5m//s)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • WORK, ENERGY & POWER

    DC PANDEY|Exercise Level 2 Subjective|15 Videos

  • WORK, ENERGY & POWER

    DC PANDEY|Exercise Level 2 Comprehension Based|2 Videos

  • WORK, ENERGY & POWER

    DC PANDEY|Exercise Level 2 objective|30 Videos

  • WAVE MOTION

    DC PANDEY|Exercise Integer Type Question|11 Videos

  • WORK, ENERGY AND POWER

    DC PANDEY|Exercise MEDICAL ENTRACES GALLERY|33 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 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 :

Knowledge Check

  • The potential energy of a particle of mass 5 kg moving in the x-y plane is given by U=-7x+24y joule, x and y being in metre. Initially at t = 0 the particle is at the origin. (0, 0) moving with a velocity of 6[2.4hat(i)+0.7hat(j)]m//s . The magnitude of force on the particle is :

    A
    25 unit
    B
    24 unit
    C
    7 unit
    D
    None of these

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

    A
    5 m/s
    B
    14 m/s
    C
    17.5 m/s
    D
    10 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

    A
    10 N
    B
    12 N
    C
    25 N
    D
    32 N

    • Similar Questions

    Explore conceptually related problems

    The potential energy of a particle of mass 5 kg moving in the - y plane is given by U = (-7«+24y) J, r and y being in metre. If the particle starts from rest from origin, then what is the speed (in m s^(-1)) of particle att = 2 s?

    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 :-

    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 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:

    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

    Home
    Profile