In the figure shown a plank of mass m is lying at rest on a smooth horizontal surface. A cylinder of same mass m and radius r is rotated to an angular speed w0 and then gently placed on the plank. It is found that by the time the slipping between the plank and the cylinder cease, 50% of total kinetic energy of the cylinder and plank system is lost. Assume that plank is long enough and `um` is the coefficient of friction between the cylinder and the plank.

(a) Find the final velocity of the plank.
(b) Calculate the magnitude of the change in angular momentum of the cylinder about its centre of mass.
(c) Distance moved by the plank by the time slipping ceases between cylinder and plank.

Answer

(a) `(romega_(0))/(4)`
`(b) (1)/(4) mr^(2) omega_(0)`
(c) `(r^(2) omega_(0)^(2))/(32 mu g)`