What happens to the gravitational force between two objects if (i) The mass of one object is doubled? (ii) The distance between the objects is doubled? (iii) The mass of both objects is doubled?

Gravitational force F = Gm₁m₂/r²

Case (i): Mass of one object is doubled i.e., m₁' = 2m₁
∴ F' = G(2m₁)m₂/r²
⇒ F' = 2F
Thus gravitational force gets doubled.

Case (ii): Distance between the objects is doubled i.e., r' = 2r
∴ F' = Gm₁m₂/(2r)²
⇒ F' = F/4
Thus gravitational force gets reduced by 4 times.
Distance between the objects is tripled i.e., r' = 3r
∴ F' = Gm₁m₂/(3r)²
⇒ F' = F/9
Thus gravitational force gets reduced by 9 times.

Case (iii): Mass of both the objects are doubled i.e., m₁' = 2m₁ and m₂' = 2m₂
∴ F' = G(2m₁)(2m₂)/r²
⇒ F' = 4F
Thus gravitational force becomes 4 times.