A disc of radius `r = 0.1 m` is rolled from a point A on a track as shown in the figure. The part AB of the track is a semi-circle of radius R in a vertical plane. The disc rolls without sliding and leaves contact with the track at its highest point B. Flying through the air it strikes the ground at point C. The velocity of the center of mass of the disc makes an angle of `30^(@)` below the horizontal at the time of striking the ground. At the same instant, velocity of the topmost point P of the disc is found to be `6 m//s` (Take `g = 10 m//s^(2)` ).

(a) Find the value of R.
(b) Find the velocity of the center of mass of the disc when it strikes the ground.
(c) Find distance AC.

Answer

(a) 1m
(b) `12 m//s`
(c) `3.6 sqrt3 m`