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The potential energy phi in joule of a p...

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`

Text Solution

Verified by Experts

The correct Answer is:
C
`F=-((del O/)/(delx)hati + (del O/)/(dely)hatj]`
`=(-3hati -4hatj)`

Since, particle was initially at rest. So, it will move in the direction of force.
We can see that initial velocity is in the directon of PO. So the particle will cross the X-axis at origin.
`K_(i) + U_(i) =K_(f) + U_(f)`
`:. 0+(3 xx 6 + 4 xx 8) =K_(f) + (3 xx 0 + 4 xx 0)`
or `K_(f) =50 J`
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