# Distance moved till rolling.

A horizontal plank having mass $$m$$ lies on a smooth horizontal surface. A sphere of same mass and radius $$R$$ is spined to an angular frequency $$\omega$$ and gently placed on the plank. If coefficient of friction between the plank and the sphere is $$\mu$$, find the distance moved by the plank till the sphere starts pure rolling on the plank. The plank is long enough. If answer is of the form $$\frac { a }{ b } \frac { { { \omega }^{ 2 }R }^{ 2 } }{ \mu g }$$, find $$a+b$$ where $$a$$ and $$b$$ are two co-primes integers.

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