Passage - III : A long horizontal plank of mass 'm' is lying on a smooth horizontal surface. A sphere of same mass 'm' and radius 'r' is spinned about its own axis with angular velocity omega_(0) and gently placed on the plank at t=0. The coefficient of friction between the plank and the sphere is mu. After some time the pure rolling of the sphere on the plank will start. Find the displacement of the plank till the sphere starts pure rolling.

Passage - III : A long horizontal plank of mass 'm' is lying on a smo

1.	Passage - III : A long horizontal plank of mass 'm' is lying on a smooth horizontal surface. A sphere of same mass 'm' and radius 'r' is spinned about its own axis with angular velocity omega_(0) and gently placed on the plank at t=0. The coefficient of friction between the plank and the sphere is mu. After some time the pure rolling of the sphere on the plank will start. Find the displacement of the plank till the sphere starts pure rolling.
Answer» `(omega_(0)^(2)r^(2))/(81mu G)` `(2omega_(0)^(2)r^(2))/(27 mu g)` `(4omega_(0)^(2)r^(2))/(81mu g)` `(2omega_(0)^(2)r^(2))/(81mug)` Answer :D