A force F = -K ( yi + aj) (where K is a positive constant) acts on a particle 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 force F on the particle is

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Solution

W= F.dr
Considering F= =K (yi+xj)

W = -K(yi+xj) . (dxi+dyj)

dW = -k(ydx + xdy)

dW = -kd(xy)

integrating both sides ,

W = -k [xy] lim from (0,0) to (a,a)

= -ka²

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k

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x y

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A force $F = - K (y i + a j)$ (where K is a positive constant) acts on a particle 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 force F on the particles is