Time?? It's quite different !!

A uniform circular disc of radius $\displaystyle{\mathcal{R}}$ is placed on a frictionless horizontal plane.Another identical disc rotating with angular velocity $\displaystyle{\omega}$ is gently placed on the top of it.The time taken to acquire the final angular velocity can be expressed as $\dfrac{a}{b} \times \dfrac{\mathcal{R} \omega}{\mu g}$ Where $\displaystyle{\mu}$ is the coefficient of friction between the plates. What is the value of $\displaystyle{a+b}$?

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