Ball, Don't Fall! - Part 2

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

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

where a,ba,b and cc are co-prime positive integers. Find a+b+ca+b+c

Details And Assumptions

  • Take g=9.8 ms2g=9.8 \ \text{m}\text{s}^{-2} in the downward direction if needed.

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