A solid sphere is set into motion on a rough horizontal surfce with a linar speed v in the forward direction and an angular speed v/R in the anticlockwise direction as shown infigure . Find the linear speed of the sphere a. where it stops rotating and b. when slipping finally ceases sand pure rolling starts.

Answer

A, B, C

Explanation

a. If we take moment at A then external torque will be zero.
`Therefore the initial angular momentum= the angular momentum after rotation stop (i.e. only linear velocity exists).
`MVxxR-(2/5)Ixxw=MV_0xxR`
`rarr MVR-2/5xxMR^2V/R=MV_0R`
`rarr V_0=(3V)/5`

b. Again after some time pure rolling starts.
Therefore `
`rarr MxV_0xxR=(2/5)MR^2xx(VR)+Mv'R`
`rarr mxx(3V)/7`