the gravitational force formula is $f = \\frac{gm_1m_2}{r^2}$, where $f$ is the force between two objects…

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?\n$r = \\frac{\\sqrt{gm_1m_2}}{f}$\n$r = \\frac{\\sqrt{gm_1m_2f}}{f}$\n$r = \\sqrt{gm_1m_2f}$\ndone

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?\n$r = \\frac{\\sqrt{gm_1m_2}}{f}$\n$r = \\frac{\\sqrt{gm_1m_2f}}{f}$\n$r = \\sqrt{gm_1m_2f}$\ndone

Answer

Explanation:

Step1: Rationalize the denominator

We have $r = \sqrt{\frac{Gm_1m_2}{F}}$. Multiply the numerator and denominator inside the square - root by $F$ to get $r=\sqrt{\frac{Gm_1m_2F}{F^2}}$.

Step2: Simplify the square - root

Using the property $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$ ($b>0$), we have $r = \frac{\sqrt{Gm_1m_2F}}{\sqrt{F^2}}$. Since $\sqrt{F^2}=F$ (assuming $F>0$), the simplified form is $r=\frac{\sqrt{Gm_1m_2F}}{F}$.

Answer:

$r=\frac{\sqrt{Gm_1m_2F}}{F}$