A particle moves counterclockwise once around a circular path of radius R centered at (R, 0) in the xy-plane. During this motion, the particle is subjected to a position-dependent force \(\vec{F} = -kx\,\hat{i}\), where k is a positive constant. Which of the following correctly describes the net work done on the particle by \(\vec{F}\) over one complete revolution, along with the correct justification?