This question involves the concept of the centripetal force.
The largest value that r can have is "2.16 m".
In order for the car to remain in contact with the track all the time, the weight of the car must be equal to the centripetal force acting on the car.
[tex]Weight = Centripetal\ Force\\\\mg = \frac{mv^2}{r}\\\\g = \frac{v^2}{r}\\\\r = \frac{v^2}{g}[/tex]
where,
r = radius = ?
v = speed = 4.6 m/s
g = acceleration due to gravity = 9.81 m/s²
Therefore,
[tex]r = \frac{(4.6\ m/s)^2}{9.81\ m/s^2}[/tex]
r = 2.16 m
Learn more about centripetal force here:
https://brainly.com/question/14249440?referrer=searchResults
The attached picture illustrates the centripetal force.
