Question

A force f=-k(yi+xj) where k is constant acts on a particle

Answer 1

Answer:hey there mate !

Step-by-step explanation:

(please assume i to be i cap and j to be j cap)

Given,

Force, F= -K(yi+xj)

As the particle moves in the x-y plane,

the displacement would be,

dr= dx i + dy j

now work done is,

W=integration( F.dr)

=>W=-K(yi+xj).(dx i + dy j)

=>W=-K(ydx+xdy)

=>W=-Kd(xy). {as ydx+xdy=dxy)

therefore, on integration,

W= -K(xy)

W=-K(a*a).

{limit from (0,0) to (a,a); will give 0 for (0,0) and a^2 for (a,a)}

W=-Ka^2. (answer)