How does doubling the mass of one object and tripling the distance between another object change the gravitational force betweem them?
FG = G M1 M2 / r2
a. Force changes by 2/3
b. Force changes by 2/9
c. Force increases by 9
d. Force decreases by 3
e. No change in force
To determine how doubling the mass of one object and tripling the distance between two objects affects the gravitational force between them, we can apply the equation for gravitational force:
FG = G * (M1 * M2) / r^2
Where:
FG is the gravitational force
G is the gravitational constant
M1 and M2 are the masses of the two objects
r is the distance between the centers of the two objects
Let's consider the changes step by step:
1. Doubling the mass of one object (let's say M1) results in multiplying M1 by 2.
New gravitational force: FG' = G * (2M1 * M2) / r^2
2. Tripling the distance between the objects results in multiplying r by 3.
New gravitational force: FG'' = G * (2M1 * M2) / (3r)^2
3. Simplifying the equation:
FG'' = G * (2M1 * M2) / (9r^2)
This can be further simplified by canceling out the factor of 9:
FG'' = G * (2M1 * M2) / 9r^2
Comparing FG'' to the original gravitational force FG, we can see that the new force is 1/9th (or 2/9) of the original force:
FG'' = FG / 9
Therefore, the answer is option (b): The gravitational force changes by 2/9.