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The potential energy of a force filed ve...

The potential energy of a force filed `vec(F)` is given by `U(x,y)=sin(x+y)`. The force acting on the particle of mass m at `(0,(pi)/4)` is

A

1

B

`sqrt2`

C

`(1)/(sqrt2)`

D

0

Text Solution

Verified by Experts

The correct Answer is:
A
`(dU)/(dx)=cos(x+y)`,
`(dU)/(dy)=cos(x+y)`
`vecF=-cos(x+y)hati-cos(x+y)hatj`
`=-cos(0+pi/4)hati-cos(0+pi/4)hatj`
`|vecF|=1`
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Knowledge Check

  • The potential energy for a force filed vecF is given by U(x,y)=cos(x+y) . The force acting on a particle at position given by coordinates (0, pi//4) is

    A
    (a) `-1/sqrt2(hati+hatj)`
    B
    (b) `1/sqrt2(hati+hatj)`
    C
    (c) `(1/2hati+sqrt3/2hatj)`
    D
    (d) `(1/2hati-sqrt3/2hatj)`

  • The potnetial energy for a force field vecF is given by U(x, y)=cos(x+y) . The force acting on a particle at the position given by coordinates (0, pi//4) is

    A
    `-(1)/(sqrt2)(hati+hatj)`
    B
    `(1)/(sqrt2)(hati+hatj)`
    C
    `((1)/(2)hati+(sqrt3)/(2)hatj)`
    D
    `((1)/(2)hati-(sqrt3)/(2)hatj)`

  • The potential energy U for a force field vec (F) is such that U=- kxy where K is a constant . Then

    A
    `vec( F)=ky hat(i)+kx hat(j)`
    B
    `kx hat(i)+ky hat(j)`
    C
    the force `vec(F)` is a conservative force
    D
    the force `vec(F)` is a non-conservative force

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