Question

The force of the gravitational attraction between two bodies is directly proportional to the mass of each body and inversely proportional to the square of distance between them. If the distance between two bodies is tripled and the mass of each is doubled, what happens to the force of gravitational attraction between them?

Answer 1

The force of gravitation between them will four - ninth the original force between them.

Explanation:

According to law of gravitation, the gravitational force between two bodies of masses M and m is expressed as F = GMm/d² ... 1 where;

G is the gravitational constant

d is the distance between the masses

If the distance between two bodies is tripled and the mass of each is doubled, then the gravitational force will become:

F2 = G(2M)(2m)/(3d)²

F1 = 4GMm/9d² ... 2

Taking the ratio of the original gravitational force to the new one we have;

F1/F = 4GMm/9d²/GMm/d²

F1/F = 4GMm/9d² * d²/GMm

F1/F = 4/9

F1 = 4/9F

This shows that if the distance between two bodies is tripled and the mass of each is doubled, the force of gravitation between them will four - ninth the original force