Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. 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 $m$. $m = \frac{fr^2}{gm}$; $m = \frac{fgm}{r^2}$; $m = \frac{r^2}{fgm}$; $m = \frac{gm}{fr^2}$

Explanation:

Step1: Start with the formula

We have the formula \( F = \frac{GMm}{r^2} \). Our goal is to solve for \( m \).

Step2: Multiply both sides by \( r^2 \)

To eliminate the denominator on the right - hand side, we multiply both sides of the equation by \( r^2 \). This gives us \( F\times r^2=\frac{GMm}{r^2}\times r^2 \), which simplifies to \( Fr^2 = GMm \).

Step3: Divide both sides by \( GM \)

Now, to isolate \( m \), we divide both sides of the equation \( Fr^2=GMm \) by \( GM \). So, \( \frac{Fr^2}{GM}=\frac{GMm}{GM} \), and since \( \frac{GM}{GM} = 1 \) (as long as \( GM
eq0 \)), we get \( m=\frac{Fr^2}{GM} \).

Answer:

\( m=\frac{Fr^2}{GM} \) (corresponding to the first option: \( m = \frac{Fr^2}{GM} \))