To find the net force on any one of the masses, we need to calculate the gravitational force exerted by the other three masses.
The formula for gravitational force between two masses is given by the equation:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force,
G is the gravitational constant (approximately 6.67430 × 10^-11 N*m^2/kg^2),
m1 and m2 are the two masses, and
r is the distance between the two masses.
In this case, the distance between the masses is the length of the side of the square (1.8) multiplied by the square root of 2 (since the diagonals of a square are equal to the side length multiplied by the square root of 2).
Let's calculate the gravitational force between two masses:
F = (6.67430 × 10^-11 * 3.5 * 3.5) / [(1.8 * sqrt(2))^2]
Simplifying the equation:
F = (6.67430 × 10^-11 * 3.5 * 3.5) / (1.8^2 * 2)
F = 6.67430 × 10^-11 * 3.5 * 3.5 / (1.8^2 * 2)
F = 4.47 × 10^-11 N
So the net force on any one of the masses is approximately 4.47 × 10^-11 N.