The formula for the force between two objects is:

[tex]\[ F = \frac{G M m}{r^2} \][/tex]

where [tex]\( M \)[/tex] and [tex]\( m \)[/tex] are the masses of the two objects, [tex]\( G \)[/tex] is a constant, and [tex]\( r \)[/tex] is the distance between them.

Solve the formula for [tex]\( m \)[/tex]:

A. [tex]\( m = \frac{F r^2}{G M} \)[/tex]

B. [tex]\( m = \frac{2}{P G M} \)[/tex]

C. [tex]\( m = \frac{E G M}{r^2} \)[/tex]

D. [tex]\( m = \frac{E r^2}{C T} \)[/tex]



Answer :

To solve the formula [tex]\( F = \frac{GMm}{r^2} \)[/tex] for [tex]\( m \)[/tex], we need to isolate [tex]\( m \)[/tex] on one side of the equation. Let's go through the steps to do this:

1. Start with the given equation:
[tex]\[ F = \frac{G M m}{r^2} \][/tex]

2. Multiply both sides of the equation by [tex]\( r^2 \)[/tex] to eliminate the denominator on the right-hand side:
[tex]\[ F r^2 = G M m \][/tex]

3. To isolate [tex]\( m \)[/tex], divide both sides of the equation by [tex]\( G M \)[/tex]:
[tex]\[ m = \frac{F r^2}{G M} \][/tex]

So, the solution for [tex]\( m \)[/tex] in terms of [tex]\( F, G, M, \)[/tex] and [tex]\( r \)[/tex] is:
[tex]\[ m = \frac{F r^2}{G M} \][/tex]

Among the given options, the correct one is:
[tex]\[ m = \frac{F r^2}{G M} \][/tex]