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

Options

A. If `mu=tantheta` then 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 `2 mg sin`
C. If `mu=(tantheta)/2` there will never be pure rolling (consider inclined plane to be long enough).
D. If incline plane is not fixed and it is on smooth horizontal surface then linear momentum of the system (wedge and sphere) can be conserved in horizontal direction.

Answer

A, D

Explanation

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