What is the relationship between the radius of circular motion and the centripetal force, if the mass undergoing the circular motion is kept constant?
Yes. The short answer is that it's right there in the formula:
The longer answer is a little more complex, since that makes it look as though the centripetal force is inversely proportional to the radius of the circle if the speed is expressed linearly as metres per second and directly proportional if the speed is measured radially as radians per second. The explanation relates to the fact that the linear distance traveled around the edge of the circle is also proportional to the radius. Over all, the greater the radius of the circle, for the same radial velocity, the greater the force.