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

We have the gravitational force formula \( F_g = \frac{G M_1 M_2}{r^2} \). Our goal is to solve for \( r \). First, we can multiply both sides of the equation by \( r^2 \) to get rid of the denominator on the right side. So we have \( F_g \cdot r^2 = G M_1 M_2 \).

Step2: Isolate \( r^2 \)

Next, we want to isolate \( r^2 \). We can divide both sides of the equation by \( F_g \) (assuming \( F_g
eq 0 \), which makes sense in the context of gravitational force between two objects). This gives us \( r^2=\frac{G M_1 M_2}{F_g} \).

Step3: Solve for \( r \)

Now, to solve for \( r \), we take the square root of both sides. Since we are looking for the positive value of \( r \) (distance can't be negative), we have \( r = \sqrt{\frac{G M_1 M_2}{F_g}} \). We can also rationalize the denominator or write it in a different form, but this is a valid expression for \( r \) in terms of \( F_g \), \( G \), \( M_1 \), and \( M_2 \).

Answer:

\( r = \sqrt{\frac{G M_1 M_2}{F_g}} \)