Question

the formula to calculate the gravitational force between two objects is $f_g=\frac{gm_1m_2}{r^2}$, where $m_1$ and $m_2$ are the masses of the objects, $g$ is the gravitational constant and $r$ is the distance between the objects. solve for the positive value of $r$ in terms of $f_g$, $g$, $m_1$ and $m_2$.

Explanation:

Step1: Start with the formula

$F_g=\frac{GM_1M_2}{r^2}$

Step2: Cross - multiply

$F_g r^2 = GM_1M_2$

Step3: Isolate $r^2$

$r^2=\frac{GM_1M_2}{F_g}$

Step4: Take the square root of both sides (positive value)

$r=\sqrt{\frac{GM_1M_2}{F_g}}$

Answer:

$r=\sqrt{\frac{GM_1M_2}{F_g}}$