A force F=−K(yi+xj) (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

While movnig from (0,0) to (a,0)Along positive x-axis, y = 0 ∴F→=−kxj^i.e.  force is in negative y-direction while displacement is in positive x-direction∴W1=0Because force is perpendicular to displacement Then particle moves from (a,0) to (a,a) along a line parallel to y-axis (x=+a) during this F→=−k(yi^+aj^)  The first component of force −kyi^ will not contribute any work because this component is along negative   x-direction (−i^) while displacement is in positive y-direction (a,0) to (a,a). The second component of forcei.e. −kaj^will perform negative work∴W2=(−kaj^)(aj^)=(−ka)(a)=−ka2So net work done on the particle W=W1+W2=0+−ka2=−ka2