Force acting on a particle moving in the x-y plane is `vecF=(y^2hati+xhatj)N`, x and y are in metre. As shown in figure, the particle moves from the origin O to point A `(6m, 6m)`. The figure shows three paths, OLA, OMA, and OA for the motion of the particle from O to A.
Now consider another situation. A force `vecF=(4hati+3hatj)N` acts on a particle of mass `2kg`. The particle under the action of this force moves from the origin to a point A `(4m, -8m)`. Initial speed of the particle, i.e., its speed at the origin is `2sqrt6ms^-1`. Figure shows three paths for the motion of the particle from O to A.

If the potential energy at O is `16J`, the potential energy at A will be

Options

A. (a) `14.5J`
B. (b) `32J`
C. (c) `24J`
D. (d) `40J`

Answer

C

Explanation

In conservative force, `W=-DeltaU=-(U_f-U_i)`
`-8=[U_f-16]`
`impliesU_f=24J`