Question

the velocity v that an object r units from the earths center must have to escape earths gravity is given by $v^{2}=\frac{2gm}{r}$, where g is a constant. solve for the objects mass m.

$m = \frac{2r}{v^{2}g}$
$m = \frac{v^{2}r}{2g}$
$m = \frac{2g}{v^{2}r}$
$m = \frac{2gr}{v^{2}}$

Explanation:

Step1: Start with the given formula

$v^{2}=\frac{2GM}{r}$

Step2: Isolate $M$

Multiply both sides by $r$: $v^{2}r = 2GM$. Then divide both sides by $2G$: $M=\frac{v^{2}r}{2G}$

Answer:

$M=\frac{v^{2}r}{2G}$ (corresponding to the second - option in the multiple - choice list)