**M** and radius **R** is thrown along a rough horizontal surface so that **initially**, it slides with a linear speed $\displaystyle{\upsilon_0}$,but **does not rotate**.
As it slides, it begins to spin and eventually rolls without slipping. The time taken to start rolling can be expressed as $\dfrac{a}{b} \times \dfrac{\upsilon_0}{\mu_k g}$ Where $\displaystyle{\mu_k}$ is the coefficient of kinetic friction between the surface and the ball .What is $\displaystyle{a+b}$?

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