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{gm}{fr^2} ) ( \bigcirc m = \frac{fr^2}{gm} ) ( \bigcirc m = \frac{r^2}{fgm} ) ( \bigcirc m = \frac{fgm}{r^2} )

Explanation:

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

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

Step2: Divide both sides by \( GM \)

To isolate \( m \), divide both sides of the equation \( Fr^2 = GMm \) by \( GM \).
\( m = \frac{Fr^2}{GM} \)

Answer:

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