Question

What happens to the force between two objects, if
(1) the mass of one object is doubled?
(2) the distance between the objects is doubled and tripled?
(3) the masses of both objects are doubled?​

Answer 1

Answer:

1) If the mass of one of the objects is doubled, then the force of gravity between them is doubled. If the mass of one of the objects is tripled, then the force of gravity between them is tripled. If the mass of both of the objects is doubled, then the force of gravity between them is quadrupled; and so on.

2)  If the distance between the two objects is doubled, then Thus, the gravitational force between the two objects becomes one-fourth. If the distance between the two objects is tripled, then Thus, the gravitational force between the two objects becomes one-ninth.

3) If the mass of both of the objects is doubled, then the force of gravity between them is quadrupled; and so on. Since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces.

Answer 2

(1) Whenever the mass of one object is doubled, the gravitational force of attraction between two objects become twice.

Let, mass of 1st object = M

Let, mass of 1st object = M 2nd one = m

Let, mass of 1st object = M 2nd one = m Distance = d

Let, mass of 1st object = M 2nd one = m Distance = d ∴ F = GMm/d²

But here, F′ = G • 2M • m/d² = 2F

(2) If the distance between the objects is doubled and tripled, the force of attraction would by decreases by four times and nine times respectively.

Initially, F = GMm/d²

Initially, F = GMm/d² 1st case:- F′′ = GMm/(2d)² = ¼(GMm/d²) = F/4

Initially, F = GMm/d² 1st case:- F′′ = GMm/(2d)² = ¼(GMm/d²) = F/4 2nd case = F′′′ = GMm/(3d)² = ⅑(GMm/d²) = F/9

(3) Of the masses of both the objects is doubled, the gravitational force of attraction will be quadrupled.

F = GMm/d²

F = GMm/d² F′′′′ = G • 2M • 2m/d² = 4(GMm/d²) = 4F