# Ball, Don't Fall! - Part 2

A solid spherical ball of radius $$r=2 \ \text{m}$$ is carefully placed on top of a fixed hemisphere of radius $$R=10 \ \text{m}$$ as shown. It is then pushed very slightly.

If the ball doesn't slip till it makes an angle $$\theta=30^{\text{o}}$$ with the vertical, then the minimum required value of coefficient of friction between the ball and the hemisphere is $\dfrac{2}{a\sqrt{b}-c}$

where $$a,b$$ and $$c$$ are co-prime positive integers. Find $$a+b+c$$

Details And Assumptions

• Take $$g=9.8 \ \text{m}\text{s}^{-2}$$ in the downward direction if needed.
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