$A$ wire is bent into the shape of a parabola given by $Y = Kx^2$. $A$ bead of mass $m$ is placed on the wire,which can slide on it without friction. Initially,when the wire is at rest,the bead is at the lowest point of the parabola. If the wire is now moved with a constant acceleration $a$ parallel to the $X$-axis,what will be the distance of the new equilibrium position of the bead from the $Y$-axis,such that it remains stationary relative to the wire?

• A
  $\frac{a}{gk}$
• B
  $\frac{a}{2gk}$
• C
  $\frac{2a}{2gk}$
• D
  $\frac{a}{4gk}$