Question

the formula for the force between two objects is $f = \frac{gmm}{r^{2}}$, 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 $m$.
$m = \frac{gm}{fr^{2}}$
$m = \frac{fr^{2}}{gm}$
$m = \frac{fgm}{r^{2}}$
$m = \frac{r^{2}}{fgm}$

Explanation:

Step1: Multiply both sides by $r^{2}$

$F\times r^{2}=\frac{GMm}{r^{2}}\times r^{2}$
$Fr^{2}=GMm$

Step2: Divide both sides by $GM$

$\frac{Fr^{2}}{GM}=\frac{GMm}{GM}$
$m = \frac{Fr^{2}}{GM}$

Answer:

$m=\frac{Fr^{2}}{GM}$ (the second - option in the multiple - choice list)