A force `F=-k(y hati + x hatj)` (where k is a positive constant) acts on a particle moving in the `x-y` plane. Starting from the origin, the particle is taken along the positive x-axis to the point `(a,0)` and then parallel to the y-axis to the point `(a,a)`. The total work done by the force F on the particle is
(a) `-2ka^(2)` , (b) `2ka^(2) , (c)`-ka^(2)` , (d) `ka^(2)`

Options

A. `-2ka^2`
B. `2ka^2`
C. `-ka^2`
D. `ka^2`

Answer

C

Explanation

`dW=vecF.dvecr=-k(yhati+xhatj)xx(dxhati+dyhatj)`
`=-k[ydx+xdy]=-kd(xy)`
`W=-kint_(0.0)^(a,a)d(xy)=-k|xy|_(0,0)^(a,a)`