A force `F=-K(yhati+xhatj)` (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

Options

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

Answer

C

Explanation

(c ) dW=F.dr`=-k(yhati+xhatj)xx(dxhati+dyhatj)`
`=-k[ydx+xdy]=-kd(xy)`
`W =- underset(((0,0)))overset(((a,a)))(int)d(xy) =-k|xy|_(((0,0)))^(((a,a))) = -ka^(2)`