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.

Which of the following is correct?

Options

A. (a) There is equal probability for the force being conservative or non-conservative.
B. (b) Conservative or non-conservative nature of force cannot be predicted on the basis of given information.
C. (c) The given force is non-conservative.
D. (d) The given force is conservative.

Answer

C

Explanation

For path `OMA`:
Path `OM: vecF=y^2hati, dx=0`
`W_(OM)=underset0overset6intvecF.dvecx=0`
Path `MA: vecF=(36hati+xhatj)N`
`W_(MA)=underset(x_1)overset(x_2)int F_xdx+underset(y_1)overset(y_2)intF_ydy, dy=0`
`=36xx6+0=216J`
`W_(OMA)=216J`
For path OLA:
Path `OL: vecF=hatj`, `dy=0`
`W_(OL)=0`
Path `LA: vecF=(y^2hati+6hatj)N`
`W_(LA)=underset(x_1)overset(x_2)int F_xdx+underset(y_1)overset(y_2)int F_ydy`
`=0+6xx(y_2-y_1)=6xx6=36J`
`:. W_(OMA)!=W_(OLA)`
Hence, force is not conservative.