The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with the above spring of half the length, the line OA will:

(a) shift toward F-axis
(b) shift towards X-axis
(c) remain as it is
(d) become double in length
If we cut the spring into half the length, the new force constant $K_{new}=2K_{org}$.
Since force is proportional to force constant(the new one). So the force must have doubled. So the line OA should shift to F. But the answer in the book is given to be (b). Can anyone explain this.