Question

how does centripetal force vary with increase in radius of circular path??

Answer 1

the larger the radius, the smaller the centripetal force, for a, the centripetal force will be greater if frequency is greater and vice versa, at a constant speed the centripetal force should be lowered if the radius is increased

Answer 2

centripetal force is the opposition force acting on an object moving in circular motion , opposing the centrifugal force (outward).
simply centripetal force acting towards centre of circular path where as centrifugal force acting outwards away from center.
hence when we increase the radius centrifugal force increases accordingly to balance it , there will be more centripetal force