The story of a mercilessly thrown sphere...

A spherical ball of mass M and radius R is thrown along a rough horizontal surface so that initially, it slides with a linear speed υ0\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 ab×υ0μkg\dfrac{a}{b} \times \dfrac{\upsilon_0}{\mu_k g} Where μk\displaystyle{\mu_k} is the coefficient of kinetic friction between the surface and the ball .What is a+b\displaystyle{a+b}?


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