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?

(N/A) According to the universal law of gravitation,the force of gravitation between two objects is given by $F = \frac{G M m}{r^{2}}$.
$(i)$ $F$ is directly proportional to the masses of the objects. If the mass of one object is doubled,then the gravitational force will also get doubled.
$(ii)$ $F$ is inversely proportional to the square of the distance between the objects. If the distance is doubled,the gravitational force becomes one-fourth of its original value. Similarly,if the distance is tripled,the gravitational force becomes one-ninth of its original value.
$(iii)$ $F$ is directly proportional to the product of the masses of the objects. If the masses of both objects are doubled,the new force $F' = \frac{G(2M)(2m)}{r^{2}} = 4 \times \frac{G M m}{r^{2}} = 4F$. Thus,the gravitational force becomes four times the original value.