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: Recall the rule of square - root simplification

For $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$ ($a\geq0,b > 0$). Given $r = \sqrt{\frac{Gm_1m_2}{F}}$, we can rewrite it as $r=\frac{\sqrt{Gm_1m_2}}{\sqrt{F}}$. But this is not in the given options. Another way is to rationalize the denominator. Multiply the numerator and denominator inside the square - root by $F$.

Step2: Rationalize the denominator

$r=\sqrt{\frac{Gm_1m_2}{F}}=\sqrt{\frac{Gm_1m_2\times F}{F\times F}}=\frac{\sqrt{Gm_1m_2F}}{F}$

Answer:

$r=\frac{\sqrt{Gm_1m_2F}}{F}$ (the second option)