Question

If the distance between two objects is increased by a factor of 3 (tripled), how will this affect Fg?

1. F g increases by 9 times
2. F g decreases to 1/9
3. F g increases by 3 times
4. F g decreases to 1/3

Answer 1

2. F g decreases to 1/9

Step-by-step explanation:

The formula for calculating the Force of gravity between two masses separated by a distance is expressed as;

F = GMm/d² ... 1

If the distance is tripled, the new force will be;

F1 = GMm/(3d)²

F1 = GMm/9d² ... 2

Divide equation 1 by 2

F/F1 = GMm/d²÷GMm/9d²

F/F1 = GMm/d²×9d²/GMm

F/F1 = 1 * 9

F = 9F1

F1 = 1/9 F

This means that the new force decreases to 1/9