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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?
Solution
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 distances between the objects. If the distance is doubled, then the gravitational force becomes one-fourth of its original value.
Similarly, if the distance is tripled, then the gravitational force becomes one-ninth of its original value.
$(iii)$ $F$ is directly proportional to the product of masses of the objects. If the masses of both the objects are doubled, then the gravitational force becomes four times the original value.