To find the magnitude of the net gravitational force on one of the masses, due to the other three, we can use Newton's law of universal gravitation.
The formula is given by:
F = (G * m1 * m2) / r^2,
where:
F is the force of gravity,
G is the gravitational constant (which is approximately 6.674 x 10^-11 N m^2/kg^2),
m1 and m2 are the masses of two objects,
r is the distance between the centers of the two objects.
In this case, the mass of each object is 900 kg and the distance between the centers of two objects is the length of the diagonal of the square.
To calculate the diagonal, we can use the Pythagorean theorem:
d^2 = s^2 + s^2,
where:
d is the length of the diagonal,
s is the length of one side of the square.
In this case, the length of one side of the square is given as 15.0 cm. Converting it to meters, we have s = 0.15 m.
Using the Pythagorean theorem, we can calculate the length of the diagonal:
d^2 = (0.15)^2 + (0.15)^2,
d^2 = 0.0225 + 0.0225,
d^2 = 0.045,
d = √(0.045),
d ≈ 0.212 m.
Now, we can calculate the magnitude of the net gravitational force on one of the masses:
F = (G * m1 * m2) / r^2,
F = (6.674 x 10^-11 N m^2/kg^2) * (900 kg) * (900 kg) / (0.212 m)^2.
Calculating this expression will give us the magnitude of the net gravitational force on one of the masses.