Distance moved till rolling.

A horizontal plank having mass m m lies on a smooth horizontal surface. A sphere of same mass and radius R R is spined to an angular frequency ω \omega and gently placed on the plank. If coefficient of friction between the plank and the sphere is μ \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 abω2R2μg \frac { a }{ b } \frac { { { \omega }^{ 2 }R }^{ 2 } }{ \mu g } , find a+b a+b where a a and b b are two co-primes integers.

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