Answer:
μ M G = Ff frictional force
M V^2 / R = centripetal force
μ G = V^2 / R condition for no slipping
R = V^2 / (μ G) (I)
T = 60 rev/min / 60 sec/min = 1 / sec period of 1 revolution
V = 2 π R / T = 2 π R speed of button
R μ G = V^2 from (I)
R μ G = 4 π^2 R^2
R = μ G / (4 π^2)
This is dimensionally correct because T = 1 sec is implicit in the equation