Two objects with masses m1 and m2 are located a distance d apart. If their masses are each doubled and the separation between them is reduced to d/2, by what factor does the gravitational force between them change?

The gravitational force between the masses will change by a factor of 16.

Explanation:

Newton's law of universal gravitation: It states that the force of attraction between two masses in the universe is directly proportional to the product of the masses and inversely proportional to the square of the distance between the masses.

It can be expressed mathematically as

F = Gm₁m₂/d² ... Equation 1

Where F = force of attraction, m₁ = mass of the first body, m₂ = mass of the second body, d = distance between the masses, G = universal constant.

From the question, if each of the masses is doubled, and the separation between them is reduced to d/2

∴ F₁ = G (2m₁*2m₂) / (d/2) ²

F₁ = G (4m₁m₂) d²/4

F₁ = 16Gm₁m₂/d² ... Equation 2

Comparing Equation 1 and 2,

F₁ = 16F

Therefore the gravitational force between the masses will change by a factor of 16.