Metallic Plate on Cylinder (A/B/2/2014)

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.