Question
The formula for the force between two objects is F=GMm/r^2
,
where M and m are the masses of the two objects, G is a constant, and r is the distance between them. Solve the formula for m.
,
where M and m are the masses of the two objects, G is a constant, and r is the distance between them. Solve the formula for m.
Answers
GPT-4o mini
To solve the formula \( F = \frac{GMm}{r^2} \) for \( m \), we can start by rearranging the equation. Here are the steps:
1. Multiply both sides by \( r^2 \) to eliminate the fraction:
\[
F r^2 = GMm
\]
2. Next, divide both sides by \( G \) to isolate \( m \):
\[
\frac{Fr^2}{G} = Mm
\]
3. Finally, divide both sides by \( M \) to solve for \( m \):
\[
m = \frac{Fr^2}{GM}
\]
Thus, the formula for \( m \) is:
\[
m = \frac{Fr^2}{GM}
\]
1. Multiply both sides by \( r^2 \) to eliminate the fraction:
\[
F r^2 = GMm
\]
2. Next, divide both sides by \( G \) to isolate \( m \):
\[
\frac{Fr^2}{G} = Mm
\]
3. Finally, divide both sides by \( M \) to solve for \( m \):
\[
m = \frac{Fr^2}{GM}
\]
Thus, the formula for \( m \) is:
\[
m = \frac{Fr^2}{GM}
\]