A wheel rolls on a plane surface without slipping. At a certain instant velocity and acceleration of center ‘O’ are  $1m/sand3m/s^2$. Radius of the wheels is 0.5 m, BD is horizontal and AC is vertical. If at that instant ratio of acceleration of point ‘C’ and that of point ‘A’ on the wheels is  $\frac{2}{\sqrt{N}}$. Find $N$.