A solid sphere is given an angular velocity `zeta` and kept on a rough fixed incline plane. The choose the correct statement.

Options

A. If `mu=tantheta`, then the sphere will be in linear equilibrium for some time and after that pure rolling down the plane will start
B. If `mu=tantheta`, then sphere will move up the plane and frictional force acting all the time will be `2mgsinrho`.
C. If `mu=tantheta//2` there will never be pure rolling (consider inclined plane to be long enough).
D. If the incline plane is not fixed at it is on the smooth horizontal surface, then the linear momentum of the system (wedge and sphere) can be conserved in the horizontal direction.

Answer

A, D

Explanation

Due to the torque of friction about CM `zeta` eventually decreases to zero, initially there is no translation. Friction is sufficient for pure rolling, therfore after sometime pure rolling begins. There is no external force in `x` direction, therefore momentum is conserved along `x` direction.