To solve this problem we will apply the concepts related to the equations of linear motion and angular motion in order to find the radius. Our values are given as,
[tex]g=9.81m/s^2[/tex]
Then
[tex]4g= 39.24 m/s^2[/tex]
The relation between the acceleration and the angular velocity and the radius is,
[tex]a_c=\omega^2*r[/tex]
The angular velocity and the lineal velocity can be related as,
[tex]v=\omega r[/tex]
The acceleration and the velocity was given, then
[tex]39.24=\omega^2 r[/tex]
[tex]600=\omega r[/tex] [tex]\rightarrow r = \frac{600}{\omega}[/tex]
Replacing at the first equation we have,
[tex]39.24 = \omega^2 (\frac{600}{\omega} )[/tex]
[tex]\omega = \frac{39.24}{600}[/tex]
[tex]\omega = 0.0654rad/s[/tex]
Now using this expression to find the radius we have that
[tex]r = \frac{600}{\omega}[/tex]
[tex]r = \frac{600}{0.0654}[/tex]
[tex]r = 9174.31 \approx 9200m[/tex]
Therefore the correct answer is C.
