A very small cube of mass `m` is placed on the inside of a conial funnelof semivertical angle `(pi//2-theta)`. The funnel is then set in rotation. If the coefficient of static friction between the cube and the funnel is `mu` and the centre of the cube is at a distance`r` from the axis of rotation, what are the largest and smallest angular velocities with which the funnel can be rotated so that the block will not move with respect to the funnel ?

Answer

`omega_(max)=sqrt((g sin theta+mu cos theta)/(r cos theta-mu sin theta)),omega_(min)=sqrt((g sin theta-mu cos theta)/(rcos theta+mu sin theta))`