State of motion of the sphere at t = 0 is described in figure, Centre of the sphere is moving towards right with a speed u and angular velocity of the sphere is u/2r in the anticlockwise sense. Here is the radius of sphere. We can understand that it is a case of slipping and after some time sphere starts pure rolling due to friction from the surface. We can assume direction towards right as positive and thus clockwise sense should be treated positive for rotational motion. Assume ng coefficient of friction between sphere and the surface. Mass of sphere is m. What will be the speed of sphere when it starts pure rolling?

State of motion of the sphere at t = 0 is described in figure, Centre

1.	State of motion of the sphere at t = 0 is described in figure, Centre of the sphere is moving towards right with a speed u and angular velocity of the sphere is u/2r in the anticlockwise sense. Here is the radius of sphere. We can understand that it is a case of slipping and after some time sphere starts pure rolling due to friction from the surface. We can assume direction towards right as positive and thus clockwise sense should be treated positive for rotational motion. Assume ng coefficient of friction between sphere and the surface. Mass of sphere is m. What will be the speed of sphere when it starts pure rolling?
Answer» `(4u)/(7)` `(3u)/(7)` `(2u)/(7)` `(U)/(7)` Solution :We can SUBSTITUTE equation (v) in equation (III) in the solution of previous part to get the following: `v=u-=(3u)/(7) RARR v=(4u)/(7)` HENCE option (a) is correct.