Exploring Centripetal Force: Does Radius Influence It?

[mani88]

Homework Statement

I'm investigating the effect of radius on centripetal force using a conical pendulum. If the length of the string and the mass is kept constant and I increase the orbital radius (assuming force is also kept constant) would the period of the conical pendulum increase or decrease???

Relevant Equations

F=mv^2/r or
F=m4pi^2r/T^2

Well i think centripetal force is inversely proportional to the radius, so I'm guessing it would decrease but not sure to be honest.

 

[haruspex]

think centripetal force is inversely proportional to the radius

In general, that depends what is held constant, linear speed or angular speed.
Which of those applies in this context? Or maybe something else?

Draw a free body diagram of the forces on the bob and write the corresponding equations.