Four 9.0kg- spheres are located at the corners of a square of side 0.60m .

Calculate the magnitude of the gravitational force exerted on one sphere which is in left and down corner of the square by the other three.
Express your answer using two significant figures.

To calculate the magnitude of the gravitational force exerted on one sphere by the other three, we can use Newton's Law of Universal Gravitation. According to this law, the magnitude of the gravitational force between two objects is given by the equation:

F = G * (m1 * m2) / r^2

where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between them.

In this case, we have four 9.0 kg spheres located at the corners of a square. Let's refer to the sphere in the left and down corner as sphere A and the other three spheres as spheres B, C, and D. Since the distance between each sphere and the sphere A is the same (the side length of the square, 0.60 m), we can calculate the gravitational force between each pair of spheres and then sum them up to find the total gravitational force on sphere A.

First, let's calculate the gravitational force between sphere A and each of the other three spheres. Using the given mass of each sphere (9.0 kg) and the distance between them (0.60 m), we can substitute these values into the formula:

F_AB = G * (m_A * m_B) / r^2
F_AC = G * (m_A * m_C) / r^2
F_AD = G * (m_A * m_D) / r^2

Now we can calculate each of these forces:

F_AB = G * (9.0 kg * 9.0 kg) / (0.60 m)^2
F_AC = G * (9.0 kg * 9.0 kg) / (0.60 m)^2
F_AD = G * (9.0 kg * 9.0 kg) / (0.60 m)^2

Next, we can sum up these forces to find the total gravitational force on sphere A:

F_total = F_AB + F_AC + F_AD

Now, we need to substitute the values of the gravitational constant and the other variables into the equation and calculate the total force. The gravitational constant G is approximately 6.674 * 10^(-11) N(m/kg)^2.

Plugging in the values, we get:

F_total = (6.674 * 10^(-11) N(m/kg)^2) * [(9.0 kg * 9.0 kg) / (0.60 m)^2] + [(9.0 kg * 9.0 kg) / (0.60 m)^2] + [(9.0 kg * 9.0 kg) / (0.60 m)^2]

Calculating this expression will give us the magnitude of the gravitational force exerted on sphere A by the other three spheres.

To calculate the magnitude of the gravitational force exerted on one sphere by the other three, we can use the formula for gravitational force:

F = G * (m1 * m2) / r^2

Where:
F is the gravitational force,
G is the universal gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2),
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of the two objects.

In this case, the mass of each sphere is 9.0 kg, and the side length of the square is 0.60 m.

We need to calculate the magnitude of the gravitational force exerted on the sphere in the left and down corner of the square by the other three spheres.

Considering two cases:

1) The sphere in the left corner, and
2) The sphere in the down corner.

1) For the sphere in the left corner:
The distance between the center of the left corner sphere and the center of the other three spheres is the diagonal of the square, which can be found using the Pythagorean theorem:

d = sqrt(s^2 + s^2)

d = sqrt(0.6^2 + 0.6^2)

d = sqrt(0.36 + 0.36)

d = sqrt(0.72)

d ≈ 0.85 m (rounded to two significant figures)

Now we can calculate the gravitational force exerted on the sphere in the left corner by the other three spheres:

F = G * (m1 * m2) / r^2

F = (6.67430 × 10^-11 N m^2/kg^2) * ((9.0 kg)^2) / (0.85 m)^2

F ≈ 2.76 × 10^-8 N (rounded to two significant figures)

2) For the sphere in the down corner:
The distance between the center of the down corner sphere and the center of the other three spheres is also the diagonal of the square, which is approximately 0.85 m as calculated above.

We can use the same formula to calculate the gravitational force exerted on the down corner sphere by the other three spheres:

F = G * (m1 * m2) / r^2

F = (6.67430 × 10^-11 N m^2/kg^2) * ((9.0 kg)^2) / (0.85 m)^2

F ≈ 2.76 × 10^-8 N (rounded to two significant figures)

Therefore, the magnitude of the gravitational force exerted on the sphere in the left and down corner of the square by the other three spheres is approximately 2.76 × 10^-8 N (rounded to two significant figures) in both cases.