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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