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The potential energy U(in J) of a partic...

The potential energy `U`(in `J`) of a particle is given by `(ax + by)`, where `a` and `b` are constants. The mass of the particle is `1 kg` and `x` and `y` are the coordinates of the particle in metre. The particle is at rest at `(4a, 2b)` at time `t = 0`.
Find the speed of the particle when it crosses x-axis

A

`2 sqrt(a^(2) + b^(2))`

B

`sqrt(a^(2) + b^(2))`

C

`(1)/(2) sqrt(a^(2) + b^(2))`

D

`sqrt(((a^(2)+b^(2)))/(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
`vec (a) = vec(F)//m =(1)/(m) ((del U)/(del X) hat i + (del U)/(del Y) hat j)`
`= -(a hat i + b j)` since, `m =1 kg`.
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Knowledge Check

  • The potential energy U (in J ) of a particle is given by (ax + by) , where a and b are constants. The mass of the particle is 1 kg and x and y are the coordinates of the particle in metre. The particle is at rest at (4a, 2b) at time t = 0 . Find the acceleration of the particle.

    A
    `4 sqrt(a^(2) + b^(2))`
    B
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    C
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    D
    `sqrt((a^(2) + b^(2)))`

  • The potential energy U (in J ) of a particle is given by (ax + by) , where a and b are constants. The mass of the particle is 1 kg and x and y are the coordinates of the particle in metre. The particle is at rest at (4a, 2b) at time t = 0 . Find the coordinates of the particle at t =1 second.

    A
    `(3.5a,1.5b)`
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    C
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    D
    (d) The coordinates of the particle at time `t=4s` are `(-18,-28)`.

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