Question

the equation shown is used to find the force of gravity, f, between two objects where: g is the gravitational constant, m1 and m2 are the masses of the two objects, r is the distance between the two objects. write an equation to correctly show the distance between the two objects. f = \frac{gm1m2}{r^2}

Explanation:

Step1: Identify the variables

The gravitational - force formula is given as $F=\frac{Gm_1m_2}{r^2}$, where $F$ is the force of gravity, $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between the two objects.

Step2: Solve for $r$

Starting with $F = \frac{Gm_1m_2}{r^2}$, we first cross - multiply to get $F\times r^2=Gm_1m_2$. Then, we divide both sides by $F$: $r^2=\frac{Gm_1m_2}{F}$. Finally, taking the square root of both sides, we have $r = \sqrt{\frac{Gm_1m_2}{F}}$.

Answer:

$r = \sqrt{\frac{Gm_1m_2}{F}}$