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
$g$.
$\bigcirc g = \frac{r^{2}}{fmm}$
$\bigcirc g = \frac{mm}{fr^{2}}$
$\bigcirc g = \frac{fmm}{r^{2}}$
$\bigcirc g = \frac{fr^{2}}{mm}$

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 \(Mm\)

$$\frac{Fr^{2}}{Mm}=\frac{GMm}{Mm}$$
$$G=\frac{Fr^{2}}{Mm}$$

Answer:

\(G = \frac{Fr^{2}}{Mm}\) (the fourth option)