Question

the gravitational force formula is $f = \frac{gm_1m_2}{r^2}$, where $f$ is the force between two objects, $g$ is the constant of gravitation, $m_1$ is the mass of the first object, $m_2$ is the mass of the second object, and $r$ is the distance between the objects. by rewriting the formula as $r = \sqrt{\frac{gm_1m_2}{f}}$, you can find the distance between objects. which of the following gives the distance, $r$, in simplest form? $r = \sqrt{\frac{gm_1m_2}{f}}$, $r = \frac{\sqrt{gm_1m_2f}}{f}$, $r = \frac{\sqrt{gm_1m_2}}{f}$

Explanation:

Step1: Start with the gravitational force formula

The formula for gravitational force is \( F=\frac{Gm_1m_2}{r^{2}} \).

Step2: Solve for \( r \)

Multiply both sides by \( r^{2} \): \( F\times r^{2}=Gm_1m_2 \).
Then divide both sides by \( F \): \( r^{2}=\frac{Gm_1m_2}{F} \).
Take the square root of both sides: \( r = \sqrt{\frac{Gm_1m_2}{F}} \).

Answer:

\( r = \sqrt{\frac{Gm_1m_2}{F}} \) (the second option in the original multiple - choice list)