Net gravitational force at the center of a square is found to be F_1 when four particles having mass M, 2 M, 3 M and 4 M are placed at the four…

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