The correct option is C −Ka2
In going from (0,0) to (a,0), the x-coordinate varies from 0 to a while the y-coordinate remains zero.
∴ Work done by force F along this path is (∵y=0)
W1=∫a0F.dx=∫a0−(Kx^j).dx^iW1=0
(∵^j.^i=0)
In going from (a,0) to (a,a), the x-coordinate remains constant at x=a while y-coordinate changes from 0 to a.
∴ Work done by force F along this path is (∵x=a)
W2=∫a0F.dy=∫a0−K(y^i+a^j).dy^j
=−Ka∫a0dyW2=−Ka2
(∵^i.^j=0,^j.^j=1)
The total work done is:
W=W1+W2=0−Ka2=−Ka2.