Question

Which factor when doubled would produce the greatest change in the centripetal force?

Answer 1

Let us consider the centripetal force equation,  
centripetal force F = mv² / r  
 f= force
 v= velocity
 m= mass
 r= radius.
 
 in all the factors only velocity has the power of 2. so when you double the velocity then it will become square of that. 
 if v= 2v , F = m4v² / r 
 so velocity is doubled it would produce the greatest change in the centripetal force.