Question

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 particles is

Answer 1

We know that,
Work done=Force x displacement
For origin to (a,0), the total work done=W
=ai[-K(yi+xj)]= - Kay=0
For (a,0) to (a,a),the work done=W'
=(aj+ai-ai).[-K(yi+xj)]= - Kax= - Ka
So the total work done
=W+W'=0 - Ka²
= - Ka²