Well, if you've got four point masses having a little square party at the corners, and they're all enjoying themselves with their gravitational forces, it's time to do some math!
Since the point masses are at the corners of a square, we can consider them to be at the vertices of an equilateral triangle. Each side of the triangle would be equal to 20 cm (since the side of the square is 20 cm).
Now, let's name our point masses for convenience. We'll call them Mass A, Mass B, Mass C, and Mass D. Let's assume that all four masses are the same and have a value of "Mass M."
Since our square is symmetric, we can see that the net gravitational force on the point mass m5 located at the center would have the same magnitude as the net force in the x-direction (horizontal) and y-direction (vertical).
In the x-direction, we have two point masses (Mass A and Mass C) at equal distances on either side of the center. Therefore, the x-component of the net gravitational force on m5 would be zero since these forces cancel out each other.
In the y-direction, we have two point masses (Mass B and Mass D) at equal distances on either side of the center. We can use Newton's law of universal gravitation to find the magnitude of the y-component of the net gravitational force on m5:
F_g = (G * Mass M * m5) / (r^2)
Where G is the gravitational constant, Mass M is the mass of each corner point mass, m5 is the mass at the center, and r is the distance between the center and each corner (which is half of the side length of the square, so 10 cm).
After calculating the force using this formula, you need to double it since two opposite point masses are creating the force. Then, you can find the magnitude of the net gravitational force on m5 by using the Pythagorean theorem:
Net Force = sqrt((x-component)^2 + (y-component)^2)
Now, enough with the heavy calculations, let's lighten up! It seems like these four point masses are having a real attraction party at that square's corners. It's a good thing that m5, the star of our show at the center, doesn't have to worry much about their gravitational force. So, sit back, relax, and enjoy the center stage, m5!