To solve the formula [tex]\( F = \frac{GMm}{r^2} \)[/tex] for [tex]\( m \)[/tex], we need to isolate [tex]\( m \)[/tex] on one side of the equation. Let's go through the steps to do this:
1. Start with the given equation:
[tex]\[
F = \frac{G M m}{r^2}
\][/tex]
2. Multiply both sides of the equation by [tex]\( r^2 \)[/tex] to eliminate the denominator on the right-hand side:
[tex]\[
F r^2 = G M m
\][/tex]
3. To isolate [tex]\( m \)[/tex], divide both sides of the equation by [tex]\( G M \)[/tex]:
[tex]\[
m = \frac{F r^2}{G M}
\][/tex]
So, the solution for [tex]\( m \)[/tex] in terms of [tex]\( F, G, M, \)[/tex] and [tex]\( r \)[/tex] is:
[tex]\[
m = \frac{F r^2}{G M}
\][/tex]
Among the given options, the correct one is:
[tex]\[
m = \frac{F r^2}{G M}
\][/tex]
