A force `F= -khati+xhatj` where k is a positive constant, acts on a praricle moving in the xy 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 formce 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)`