Home
Class 12
PHYSICS
The potential energy varphi, in joule, o...

The potential energy `varphi`, in joule, of a particle of mass `1kg`, moving in the x-y plane, obeys the law `varphi=3x+4y`, where `(x,y)` are the coordinates of the particle in metre. If the particle is at rest at `(6,4)` at time `t=0`, then

A

its acceleration is of magnitude `5m//s^(2)`

B

its speed when it crosses the y-axis is `10m//s`

C

it crosses the y-axis `(x=0)` at `y = -4`

D

it moves in a striaght line passing through the origin `(0, 0)`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
`U = 3x +4y`
`a_(y)=(F_(y))/(m)=(-(del Uf delx))/(m)=-3`
`a_(x) = (F_(y))/(m)=(-(delU//dely))/(m) =-4`
`rArr |a|=5m//s_(2)`
Let at time 't' particle crosses y-axis
Then `-6 = (1)/(2)(-3)t_(2) rArr t = 2sec`
Along y-direction : `Delta y=(1)/(2) (-4)(2)_(2)=-8`
`rArr` particle crosses y-axis at y = -4
At `(6,4)U = 34` & `KE = 0`
At `(0,-4) U = -16 rArr KE = 50`
or `(1)/(2) mv_(2) = 50 rArr v = 10 m//s`
while crossing y-axis `v = 10 m//s`.
Promotional Banner

Topper's Solved these Questions

  • DAILY PRACTICE PROBLEM

    RESONANCE ENGLISH|Exercise DPP No.27|20 Videos

  • DAILY PRACTICE PROBLEM

    RESONANCE ENGLISH|Exercise DPP No.28|9 Videos

  • DAILY PRACTICE PROBLEM

    RESONANCE ENGLISH|Exercise DPP No.25|20 Videos

  • CURRENT ELECTRICITY

    RESONANCE ENGLISH|Exercise High Level Problems (HIP)|19 Videos

  • ELECTRO MAGNETIC WAVES

    RESONANCE ENGLISH|Exercise Exercise 3|27 Videos

Similar Questions

Explore conceptually related problems

The potential energy U in joule of a particle of mass 1 kg moving in x-y plane obeys the law U = 3x + 4y , where (x,y) are the co-ordinates of the particle in metre. If the particle is at rest at (6,4) at time t = 0 then :

The potential energy phi in joule of a particle of mass 1 kg moving in x-y plane obeys the law, phi=3x + 4y . Here, x and y are in metres. If the particle is at rest at (6m, 8m) at time 0, then the work done by conservative force on the particle from the initial position to the instant when it crosses the x-axis is . a) 25 J b) 25 J c) 50 J d) - 50 J

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 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 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

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 particle is moving along the x-axis whose acceleration is given by a= 3x-4 , where x is the location of the particle. At t = 0, the particle is at rest at x = 4//3m . The distance travelled by the particles in 5 s is

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 :

athe potential energy of a particle of mass 2 kg moving along the x-axis is given by U(x) = 4x^2 - 2x^3 ( where U is in joules and x is in meters). The kinetic energy of the particle is maximum at

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