Question

the formula to calculate the gravitational force between two objects is $f_g = \frac{g m_1 m_2}{r^2}$, 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 $m_2$ in terms of $f_g$, $g$, $m_1$ and $r$.

Explanation:

Step1: Multiply both sides by \( r^2 \)

To isolate the term with \( M_2 \), we multiply both sides of the equation \( F_g = \frac{G M_1 M_2}{r^2} \) by \( r^2 \). This gives us \( F_g r^2 = G M_1 M_2 \).

Step2: Divide both sides by \( G M_1 \)

Now, to solve for \( M_2 \), we divide both sides of the equation \( F_g r^2 = G M_1 M_2 \) by \( G M_1 \). So, \( M_2 = \frac{F_g r^2}{G M_1} \).

Answer:

\( \frac{F_g r^2}{G M_1} \)