Given equation is F=mv * v/R

what is the relationship exist between F and R?

This is called an "inverse" relationship because the bigger R becomes, the smaller F becomes as a result. you can do a couple of calculations on your calculator to see this (just increase R and watch what happens to F).

Also, when an equation has F = (x. y) / R^2 we call this the "inverse square" relationship, since it is also inverse, but squared. In practice it means that every time you double R, F decrease by 4 times! You will see this in physics a lot, so it's good to know!