What happens to the force between two objects, if the mass of one object is doubled?

According to Newton’s law of universal gravitation, the force of attraction between two objects is directly proportional to the product of their masses. Thus, if the mass of one object is doubled while keeping the other object’s mass and the distance between them constant, the gravitational force between the two objects will also double.

This is consistent with the formula for gravitational force:

F = (G.m₁.m₂)/(r²)

Where:
– F is the gravitational force.
– G is the gravitational constant.
– m₁ and m₂ are the masses of the two objects.
– r is the distance between their centers.

When one mass is doubled, let’s say m₁, the new force becomes:

F’ = (G.(2m₁).m₂)/(r²)

F’ = 2. (G.(2m₁).m₂)/(r²)

F’ = 2

Therefore, doubling the mass of one object in the gravitational interaction results in a doubling of the gravitational force between the two objects while all other factors remain constant. This illustrates the direct relationship between the masses and the gravitational force as described by Newton’s law of universal gravitation.