A Nonlinear Spring Generates a Force $f = \beta x ^ { 2 }$

Multiple Choice

A nonlinear spring generates a force $f = \beta x ^ { 2 }$ , where $\beta$ is a constant and $x$ is the distance that the spring is compressed or stretched. The spring hangs from the ceiling, and a mass $m$ is attached to the other end of the spring. The distance that the spring is stretched is

A) $\beta / ( m g )$
B) $\sqrt { m g / \beta }$
C) $\beta \sqrt { m g }$
D) $\sqrt { \beta / m / g }$