A solid sphere is set into motion on a rough horizontal surface with a linear speed u in the forward direction and an angular speed u/R in the anticlockwise direction as shown in figure (10-E 16). Find the linear speed of the sphere (a) when it stops rotating and (b) when slipping finally ceases and pure rolling starts.

A thin spherical shell lying on a rough horizontal surface is hit by a cue in such a way that the line of action passes through the center of the shell. As a result, the shell starts moving with a linear speed u without any initial angular velocity. Find the linear speed of the shell after it starts pure rolling on the surface.

A hollow sphere of radius R lies on a smooth horizontal surface. It is pulled by a horizontal force acting tangentially from the highest point. Find the distance travelled by the sphere during the time it makes one full rotation.

A solid sphere of mass 0.50 kg is kept on a horizontal surface. The coefficient of static friction between the surfaces in contact is 2/7. What maximum force can be applied at the highest point in the horizontal direction so that the sphere does not slip on the surface?

A solid sphere rolling on a rough horizontal surface with a linear speed u collides elastically with a fixed, smooth, vertical wall, Find the speed of the sphere after it has started pure rolling in the backward direction.