1. Understand the Forces

* Gravitational Force: This force attracts any two objects with mass. It is calculated using Newton's Law of Universal Gravitation:

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

* Where:

* G = Gravitational constant (6.674 x 10^-11 N m^2/kg^2)

* m1, m2 = masses of the objects

* r = distance between the centers of the objects

* Electrical Force: This force attracts or repels charged objects. It is calculated using Coulomb's Law:

* F_electric = (k * q1 * q2) / r^2

* Where:

* k = Coulomb's constant (8.98755 x 10^9 N m^2/C^2)

* q1, q2 = charges of the objects

* r = distance between the centers of the objects

2. Set the Forces Equal

We want the electrical force to equal the gravitational force:

F_gravity = F_electric

(G * m1 * m2) / r^2 = (k * q1 * q2) / r^2

3. Simplify and Solve for Charge

* The distance 'r' cancels out on both sides.

* Since the masses are equal (m1 = m2 = 100 kg) and the charges are equal (q1 = q2 = q), we can simplify further:

G * m^2 = k * q^2

Solve for q:

q^2 = (G * m^2) / k

q = √((G * m^2) / k)

4. Plug in Values and Calculate

q = √((6.674 x 10^-11 N m^2/kg^2 * (100 kg)^2) / (8.98755 x 10^9 N m^2/C^2))

q ≈ 8.61 x 10^-6 C

Answer:

Each spherical mass must have a charge of approximately 8.61 microCoulombs (µC) for the electrical force to equal the gravitational force.

Important Note: This calculation assumes that the spheres are point charges. In reality, the charge distribution on the spheres will affect the electric force.