For the position of button we can use force balance as
Friction Force = Centripetal force
so here we will have

here we know that
R = radius of circle where button is placed

f = 35 rev/min


now from above equation


so friction coefficient will be 0.33
As per Newton's II law we know that

here F = force applied
m = mass of object = 2 kg
a = acceleration = 2 m/s^2
now as per above formula we will have


so here applied force on the ball will be 4 N
5.5 is the answer i think