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.

Work done for motion along path OA is nearly

Options

A. (a) `383J`
B. (b) `90J`
C. (c) `180J`
D. (d) None of these

Answer

B

Explanation

`W_(OA)=int F_xdx+intF_ydy`
`=underset0overset6inty^2dx+underset0overset6intxdy`, for this path: `y=x`
`=underset0overset6intx^2dx+underset0overset6intydy=[x^3/3]_0^6+[y^2/2]_0^6=90J`