(i) We know,

F = G $\dfrac{\text{m}_1\text{m}_2}{\text{d}^2}$

Where,

F = force of attraction

G = constant of proportionality

m₁ = mass of first object

m₂ = mass of second object

d = distance between the two objects.

When mass of one object is doubled.

m' = 2m₁

So, substituting we get,

F' = G $\dfrac{\text{2m}_1\text{m}_2}{\text{d}^2}$ = 2G $\dfrac{\text{m}_1\text{m}_2}{\text{d}^2}$ = 2F

Hence, when the mass of one object is doubled, the gravitational force increases two times.

(ii) When distance is doubled then, d' = 2r

So, substituting we get,

F' = G $\dfrac{\text{m}_1\text{m}_2}{(2d)^2}$ = G $\dfrac{\text{m}_1\text{m}_2}{4d^2}$ = $\dfrac{\text{F}}{4}$

Hence, when the distance between the objects is doubled, the gravitational force becomes one fourth of its original force.

Now, if it's tripled

d' = 3r

So, substituting we get,

F' = G $\dfrac{\text{m}_1\text{m}_2}{(3d)^2}$ =G $\dfrac{\text{m}_1\text{m}_2}{9d^2}$ = $\dfrac{\text{F}}{9}$

Hence, when the distance between the objects is tripled, the gravitational force becomes one ninth of its original force.

(iii) If masses of both the objects are doubled, then

m₁' = 2m₁

and

m₂' = 2m₂

So, substituting we get,

F' = G $\dfrac{\text{2m}_1\text{2m}_2}{\text{d}^2}$ = 4G $\dfrac{\text{m}_1\text{m}_2}{\text{d}^2}$ = 4F

Hence, when the masses of both the objects are doubled, the gravitational force becomes four times the original force.

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