A uniform metallic plate of negligible thickness, mass \( 2m\) and length \(4R\) is twisted in the middle forming a right angle.The twisted plate is then placed on a cylinder of radius \(R\) which lies fixed (unable to move ) on the horizontal plane. There is static friction between the cylinder and the plate.

The minimum coefficient of static friction \(\mu_s\) in order the plate to be in equilibrium can be expressed as:

\(\mu_s = \sqrt{a} - b \)

Where \(a\) and \(b\) are co-prime square free integers.

*Find the value of \(a+b\)*

**Assumptions**

Use \(g\) , the gravitational acceleration \( 9.8 m/s^2 \) if needed.

*Note:*
This problem was part of the Greek National Physics Contest 2014.

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