Two point charges, initially 1 cm apart, are moved to a distance of 3 cm apart. by what factor do the resulting electric and gravitational forces between them change? a.9 c.1/3 b.3 d.1/4

1/9

Explanation:

As per Coulomb Law, electric force, is inversely related to the square of the distance that separate them., when other factors remain constant.

That means, Electrical force α 1/d^2, => Electrical force = k / d^2

Call FE the electrical force when d = 1 cm => FE = k / (1cm)^2

Call FE' the electrical force when d = 3cm => FE' = k / (3cm)^2

=> k = FE(1cm)^2 = FE'(9cm)^2 => FE' = FE / 9

As per Universal Gravitational Law, discovered by Sir Isacc Newton, the gravitational force between two objects is inversely related to the square of the distance that separate them, so you get the same relation between the gravitational force and the distance as you found for the electric force,i.e  gravitational force α 1/d^2, with which you will obtain the same factor for the case given: 1/9.