Question

multiple choice question
which formula defines gravitational mass—an objects response to gravitational force?
\\( m_g = \frac{gfg}{r2} \\)
\\( m_g = \frac{r2 fg}{gm} \\)
\\( m_g = \frac{gmfg}{r2} \\)
\\( m_g = \frac{r2 fg}{g} \\)

Explanation:

Step1: Recall Newton's law of gravitation

Newton's law of gravitation is $F_g = G\frac{m_g M}{r^2}$, where $F_g$ is gravitational force, $G$ is gravitational constant, $m_g$ is gravitational mass of the object, $M$ is mass of the other body, and $r$ is distance between them.

Step2: Rearrange the formula to solve for $m_g$

Multiply both sides by $r^2$: $F_g r^2 = G m_g M$. Divide both sides by $G M$: $m_g = \frac{r^2 F_g}{G M}$.

Answer:

$m_g = \frac{r2 Fg}{Gm}$ (assuming the second option has a typo where $M$ is written as $m$)