Net gravitational force at the center of a square is found to be $F_1$ when four particles having mass M , $2 \mathrm{M}, 3 \mathrm{M}$ and 4 M are placed at the four corners of the square as shown in figure and it is $F_2$ when the positions of 3 M and 4 M are interchanged. The ratio $\frac{F_1}{F_2}$ is $\frac{\alpha}{\sqrt{5}}$. The value of $\alpha$ is $\_\_\_\_$ .