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

(i)

According to universal law of gravitation, the force between 2 objects (m₁ and m₂) is proportional to their plenty and reciprocally proportional to the sq. of the distance(R) between them.

If the mass is doubled for one object.

F = 2F, so the force is also doubled.

(ii)

If the distance between the objects is doubled and tripled

If it’s doubled

Hence,

F = (Gm₁m₂)/(2R)²

F = 1/4 (Gm₁m₂)/R²

F = F/4

Force thus becomes one-fourth of its initial force.

Now, if it’s tripled

Hence,

F = (Gm₁m₂)/(3R)²

F = 1/9 (Gm₁m₂)/R²

F = F/9

Force thus becomes one-ninth of its initial force.

(iii)

If masses of both the objects are doubled, then

F = 4F, Force will therefore be four times greater than its actual value.