Let me try to be even more clear.
Consider this :-
By Newton's laws a particle of mass m in uniform circular motion experiences a centripetal force equal to m v^2 / r ( v is the uniform speed and r is the radius of the circle ) . Now start inflating the circle by
increasing it's radius more than any fixed value (namely make the radius tend to infinite value)
No problem so far. The mass point's trajectory approaches a straight line. The centripetal force approaches zero because the radius is infinite in the denominator, and m and v are finite constants in the numerator (because you assumed uniform rotation). All is well in the world of Newtonian physics.
and now , for the particle , choose it such that the quantity mv^2 = momentum x velocity such that mv^2 ~ br (b being a nonzero finite quantity) ; [/quote]
But this is where you cause problems for yourself by assuming unphysical conditions. Without an infinite force or an infinite amount of time at your disposal, how are you going to increase mv^2 to an infinite value?