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 $m$.\
\bigcirc $m = \frac{r^2}{fgm}$\
\bigcirc $m = \frac{fgm}{r^2}$\
\bigcirc $m = \frac{gm}{fr^2}$\
\bigcirc $m = \frac{fr^2}{gm}$

Explanation:

Step1: Start with the formula \( F = \frac{GMm}{r^2} \)

We need to solve for \( M \), so first, multiply both sides by \( r^2 \) to get rid of the denominator on the right.
\( F \times r^2 = GMm \)

Step2: Isolate \( M \)

Now, divide both sides by \( Gm \) to solve for \( M \).
\( M = \frac{Fr^2}{Gm} \)

Answer:

\( M = \frac{Fr^2}{Gm} \) (the last option: \( M = \frac{Fr^2}{Gm} \))