(i) If the mass of one object is doubled, the force of attraction between the two objects also doubles. This is because the force of gravity is directly proportional to the product of the masses of the objects.
(ii) If the distance between two objects is doubled, the force between them becomes one-fourth of the original force. If the distance is tripled, the force becomes one-ninth of the original force. This is due to the inverse square relationship between gravitational force and the square of the distance between objects.
Explanation:
Inverse Square Relationship:
The force of gravity between two objects is inversely proportional to the square of the distance between them. This means that as the distance increases, the force decreases rapidly.
Doubling the Distance:
When the distance between two objects is doubled, the distance squared increases by a factor of 4 (2 x 2 = 4). Since the force is inversely proportional to the square of the distance, the force becomes one-fourth of its original value.
Tripling the Distance:
When the distance is tripled, the distance squared increases by a factor of 9 (3 x 3 = 9). Consequently, the force becomes one-ninth of its original value. (iii) If the masses of both objects are doubled, the gravitational force between them becomes four times the original force. This is because the force is directly proportional to the product of the masses. When both masses are doubled, their product increases by a factor of 4 (2 * 2).