Gravitation: JEE Main 2026 Physics question

Net gravitational force at the center of a square is found to be $F_1$ when four particles having mass $M$, $2M$, $3M$ and $4M$ are placed at the four corners of the square as shown in figure and it is $F_2$ when the positions of $3M$ and $4M$ are interchanged. The ratio $\frac{F_1}{F_2}$ is $\frac{\alpha}{\sqrt5}$. The value of $\alpha$ is ______.