Answer:

Introduction:
In this question, we have to find out how many electrons must be removed from each of two 5kg copper spheres to make the electric forces of repulsion between them equal in magnitude to the gravitational forces of attraction between them.

Calculating gravitational force and electric force:
To calculate the gravitational force between two 5kg copper spheres, we use the formula for gravitational force which is given by:

Fg = G (m1m2)/r^2

Where,
Fg = gravitational force
G = gravitational constant (6.67 x 10^-11 Nm^2/kg^2)
m1 and m2 = masses of the two spheres (5kg each)
r = distance between the centers of the two spheres

Now, substituting the values in the formula, we get:

Fg = (6.67 x 10^-11) x (5 x 5)/r^2
Fg = 1.67 x 10^-9 N

To calculate the electric force between the two spheres, we use the formula for electric force which is given by:

Fe = k (q1q2)/r^2

Where,
Fe = electric force
k = Coulomb's constant (9 x 10^9 Nm^2/C^2)
q1 and q2 = charges on the two spheres
r = distance between the centers of the two spheres

As the two spheres are made of copper, we know that copper is a neutral element with equal numbers of protons and electrons. Therefore, the charges on the spheres are equal and opposite, and we can write:

q1 = -q2

Substituting this in the formula for electric force, we get:

Fe = k q1^2/r^2

We want the electric force to be equal to the gravitational force, so we can equate the two equations:

Fe = Fg
k q1^2/r^2 = G (m1m2)/r^2

Cancelling out r^2 from both sides, we get:

k q1^2 = G (m1m2)

Solving for q1, we get:

q1 = sqrt(G m1m2/k)

Substituting the values, we get:

q1 = sqrt((6.67 x 10^-11) x (5 x 5)/(9 x 10^9))
q1 = 1.18 x 10^-7 C

As the charge on each sphere is -q1, we can say that each sphere has lost 1.18 x 10^-7 C of electrons.

Conclusion:
Therefore, to make the electric forces of repulsion between two 5kg copper spheres equal in magnitude to the gravitational forces of attraction between them, we need to remove 1.18 x 10^-7 C of electrons from each sphere.