Friction, you make my head right round!

A sphere of mass $$\displaystyle\text{m}$$ and radius $$\displaystyle R$$ is placed on a rough plank of mass $$\displaystyle \text{2m}$$. This system is placed on a rough inclined plane, with an incline of $$\displaystyle \theta$$.

The friction coefficient between the plank and the incline is $$\displaystyle\mu_1$$, and that between sphere and plank is $$\displaystyle \mu_2$$.

Find the maximum value of $$\displaystyle \frac{\mu_1}{\mu_2}$$, such that the sphere is always pure rolling on the plank.

Details and Assumptions:
$$\bullet$$ $$\displaystyle m = 2kg$$
$$\bullet$$ $$\displaystyle \theta = 30^o$$
$$\bullet$$ $$\displaystyle R = 15cm$$
$$\bullet$$ $$\displaystyle g = 9.8m/s^2$$

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